Després de sopar, la cassola queda bruta i el forn també.

Because després de + infinitive is a very common Catalan pattern meaning after doing something.

• després de sopar = after dinner / after eating dinner
• després de dinar = after lunch
• després de treballar = after working

If you say després del sopar, then sopar is a noun: after the dinner / after dinner as an event or meal. That is possible too, but it is slightly different in structure.

So here:

• després de sopar = after having dinner

This is very similar to Spanish después de cenar.

Here, sopar is an infinitive verb, meaning to have dinner / to eat dinner.

Catalan often uses an infinitive after a preposition:

• abans de sortir = before leaving
• després de sopar = after having dinner

But sopar can also be a noun:

• el sopar = dinner

So the same form can be either:

• sopar = to have dinner
• el sopar = dinner

In your sentence, because it comes after de and has no article, it is understood as a verb.

Quedar and estar can both appear in contexts like this, but they are not exactly the same.

• està bruta = it is dirty
• queda bruta = it ends up dirty / it gets left dirty / it remains dirty

In this sentence, queda suggests the result after dinner: the casserole dish is left in a dirty state.

So:

• la cassola està bruta = the casserole dish is dirty
• la cassola queda bruta = the casserole dish ends up dirty / is left dirty

That makes queda sound a bit more natural here, because the sentence describes what happens after dinner.

Here quedar means something like:

• to end up
• to be left
• to remain

It is a very flexible verb in Catalan. Some examples:

• La porta queda oberta. = The door is left open.
• Després de ploure, el carrer queda mullat. = After it rains, the street ends up wet.
• La cuina queda neta. = The kitchen is left clean.

So in your sentence:

• la cassola queda bruta = the casserole dish is left dirty / ends up dirty

Because bruta agrees with la cassola, which is a feminine singular noun.

Catalan adjectives usually agree in gender and number with the noun they describe:

• el forn brut = the dirty oven
• la cassola bruta = the dirty casserole dish
• els plats bruts = the dirty plates
• les tasses brutes = the dirty cups

In your sentence, cassola is feminine singular, so the adjective must also be feminine singular:

• la cassola queda bruta

Catalan uses definite articles very often, including in places where English might or might not use the.

Here:

• la cassola = the casserole dish
• el forn = the oven

The articles identify the specific objects being talked about. In normal Catalan, leaving them out would usually sound wrong in this sentence.

So:

• la cassola queda bruta
• el forn també

are the natural forms.

Because Catalan, like English, often omits repeated material when it is easy to understand.

The full version would be:

• Després de sopar, la cassola queda bruta i el forn també queda brut.

But that sounds repetitive. So Catalan leaves out the repeated part:

• i el forn també

This means:

• and the oven too
• understood: and the oven is left dirty too

This kind of ellipsis is very common.

També means also / too. In Catalan, it can appear in different positions, but placing it at the end here is very natural because it modifies the whole second idea:

• i el forn també = and the oven too

You could also hear:

• i també el forn

But in this sentence, i el forn també sounds especially natural and idiomatic.

Because Catalan avoids repetition when the meaning is obvious.

If you wanted the fully expanded version, it would be:

• Després de sopar, la cassola queda bruta i el forn també queda brut.

But since queda brut is understood from the first part, it is omitted.

Notice something important: even though bruta is feminine for cassola, the omitted adjective with forn would be brut, because forn is masculine.

So the hidden full meaning is:

• la cassola queda bruta
• el forn també queda brut

Not exactly. Cassola usually refers to a cooking pot, pan, casserole dish, or earthenware cooking vessel, depending on context.

So the best English translation depends on the situation. It does not always mean the prepared food called a casserole in English.

In this sentence, la cassola is most likely the cooking dish or pot that gets dirty after dinner.

The core structure is:

• la cassola queda bruta
• i el forn també

At the beginning, Després de sopar is a time expression meaning after dinner. It is placed first to set the scene.

So the sentence is basically:

1. Després de sopar = time phrase
2. la cassola queda bruta = main statement
3. i el forn també = second coordinated statement

This is a very normal word order in Catalan.

Because Després de sopar is an introductory time phrase. Writing a comma after a fronted phrase like that is very common and helps readability.

So:

• Després de sopar, la cassola queda bruta...

is a natural written form.

In speech, there is often a small pause there too.

A more explicit version would be:

• Després de sopar, la cassola queda bruta i el forn també queda brut.

Or with estar instead of quedar:

• Després de sopar, la cassola està bruta i el forn també està brut.

These are grammatically fine, but the original sentence is more natural because it avoids unnecessary repetition.

So the given sentence is compact, idiomatic, and very typical Catalan.