Пусть фасоль и варится долго, суп с фасолью всё равно получается вкусным.

Here пусть does not mean let in the command sense.

In this sentence, пусть introduces a concession:
Пусть фасоль и варится долго, ... = Even though beans take a long time to cook, ... / Granted that beans cook for a long time, ...

This is a common pattern in Russian:

Пусть / пускай ... , всё равно ...
= Even if / although ... , still / all the same ...

So the idea is:

• пусть фасоль и варится долго = even though the beans take a long time to cook
• суп ... всё равно получается вкусным = the soup still turns out tasty

This use of пусть is quite different from the imperative-like Пусть он войдёт = Let him come in.

That и is part of a very common concessive pattern. It helps emphasize the contrast:

Пусть X и Y, Z всё равно ...
= Even though X does Y, Z still ...

So here:

• пусть ... и варится долго = even though it does cook for a long time
• всё равно in the second clause completes the contrast: still / nevertheless

The и is not the normal and here. It is more like an emphatic particle inside the concessive structure.

A good way to feel the pattern is:

• Пусть это и трудно, я попробую.
  Even though it is difficult, I’ll try.

• Пусть он и опоздал, мы его подождали.
  Even though he was late, we waited for him.

So in your sentence, и helps create the meaning admittedly / even though.

Вариться is the intransitive/reflexive form meaning to be boiled / to cook.

Compare:

• Я варю фасоль.
  I am boiling beans.
  Here варю is transitive: someone is cooking something.

• Фасоль варится долго.
  Beans take a long time to cook / The beans boil for a long time.
  Here the beans are the subject, so Russian naturally uses вариться.

English often uses cook intransitively:
Beans cook slowly.

Russian commonly uses the reflexive verb here:
Фасоль варится долго.

So варится is exactly what you would expect when the food item itself is the subject.

Because the sentence describes a general property or ongoing process, not a single completed event.

Фасоль варится долго means:
Beans take a long time to cook / Beans cook slowly

This is about duration and characteristic behavior, so the imperfective is natural.

If you used a perfective verb, it would point more toward a specific completion, something like got cooked or finished cooking, which is not the point here.

Russian often uses the imperfective when talking about:

• general truths
• repeated situations
• process
• duration

Since долго focuses on how long the cooking process lasts, the imperfective варится is the right choice.

Всё равно means all the same, still, nevertheless.

It signals that the second clause remains true despite what was said in the first clause.

So the logic is:

• Фасоль варится долго = that may be inconvenient
• суп ... всё равно получается вкусным = but despite that, the result is still good

In English, you would usually translate it as:

• still
• nevertheless
• all the same

This word pair is very common in concessive sentences, especially with пусть:

• Пусть это и дорого, я всё равно куплю.
  Even though it’s expensive, I’ll buy it anyway.

In your sentence, всё равно is a strong clue that the whole structure means even though ..., still ...

Because after получаться meaning to turn out, Russian often uses the instrumental case for the result state.

So:

• получается вкусным = turns out tasty
• вкусным is instrumental singular masculine, agreeing with суп

This is similar to other verbs of becoming or result:

• стать известным = to become famous
• оказаться полезным = to turn out to be useful
• получиться хорошим = to turn out good

Why masculine? Because суп is masculine.

Why instrumental? Because Russian often marks the predicate noun/adjective with instrumental after verbs like:

• быть in some contexts
• стать
• оказаться
• получиться / получаться

You may also sometimes hear nominative in some constructions in modern Russian, but with получаться + adjective, instrumental is very standard and natural.

Both are possible, but they are not exactly the same in feel.

• суп с фасолью = soup with beans
• фасолевый суп = bean soup

Суп с фасолью is more transparent and literal: it emphasizes that beans are one of the ingredients in the soup.

Фасолевый суп is a more fixed compound-style name, like bean soup in English.

In this sentence, суп с фасолью works well because the first clause already talks about фасоль directly, so the repetition feels natural:

• Пусть фасоль и варится долго, суп с фасолью всё равно получается вкусным.

It keeps the focus on beans as the ingredient that takes a long time to cook.

Yes, and this is a very common difference between English and Russian.

In Russian, фасоль is often treated as a mass/collective noun, so singular is normal when talking about beans as a food category or ingredient.

So:

• Фасоль полезна. = Beans are healthy.
• Я люблю фасоль. = I like beans.
• Фасоль варится долго. = Beans take a long time to cook.

English often uses the plural beans, but Russian very naturally uses singular фасоль for the general substance/ingredient.

If you wanted to speak about individual beans or kinds of beans in a more countable way, the wording would change, but here the singular is exactly what you would expect.

С фасолью uses the instrumental case.

The preposition с can take different cases depending on meaning, but in the sense with, it takes the instrumental:

• с фасолью = with beans
• с мясом = with meat
• с рисом = with rice

So the base noun is:

• фасоль

and the instrumental singular form is:

• фасолью

That is why the phrase is суп с фасолью.

Yes, the word order can vary, but the given order sounds natural and highlights the contrast well.

Current sentence:

Пусть фасоль и варится долго, суп с фасолью всё равно получается вкусным.

This structure is effective because:

• the first clause presents the drawback: beans take a long time to cook
• the second clause presents the positive outcome: the soup still turns out tasty

Russian word order is flexible, but information structure matters.
For example, you could also say:

Пусть фасоль и долго варится, суп с фасолью всё равно получается вкусным.

That is also natural. It places a little more emphasis on долго.

You could even replace пусть with another concessive connector:

Хотя фасоль варится долго, суп с фасолью всё равно получается вкусным.

That may be easier for learners to recognize, but it is slightly different in tone. The original пусть ... и ... всё равно ... has a nice concessive, slightly rhetorical flavor.

Most naturally, it sounds like a general statement:

Even though beans take a long time to cook, bean soup still turns out tasty.

Several things point to that:

• варится is imperfective and describes a general characteristic
• получается also sounds habitual/general here
• there is no context marking one specific pot of soup

So this feels like a general observation or comment about cooking.

If you wanted to talk about one specific soup being made right now, Russian would usually give more context, for example with time adverbs or a clearer situational frame.