На ужин мы запекали баклажаны, кабачки и кукурузу на большом противне.

Here На ужин means for dinner.

Russian often uses на + accusative to mean something like for a meal / for an occasion:

• на завтрак — for breakfast
• на обед — for lunch
• на ужин — for dinner

So На ужин мы запекали... means For dinner, we roasted/baked...

It is not mainly about the time of day (at dinner), but about what the food was prepared for.

Yes, Russian could leave it out.

The verb запекали already shows we, because it is past tense plural. So:

• Запекали баклажаны... = We were baking/roasting eggplants...
• Мы запекали баклажаны... = same basic meaning, but мы is more explicit

Russian often omits subject pronouns when they are clear from the verb. Including мы can add a little emphasis or simply make the sentence feel slightly more explicit.

This is a question of aspect.

• запекали = imperfective past
• запекли = perfective past

запекали presents the action as a process, repeated action, or simply without focusing on completion.
запекли would present it as a completed whole: we baked/roasted and finished doing it.

So:

• Мы запекали овощи = we were roasting vegetables / we roasted vegetables
• Мы запекли овощи = we roasted the vegetables completely / we finished roasting them

In this sentence, запекали gives a more descriptive, background-style statement about what was being made for dinner.

In the past tense, Russian verbs agree with gender/number, not person.

The basic past-tense ending here is plural:

• запекал — masculine singular
• запекала — feminine singular
• запекало — neuter singular
• запекали — plural

Since мы is plural, the verb is запекали.

So the verb form itself does not literally contain a special we ending the way present tense does, but plural past tense strongly matches мы here.

They are in the accusative plural, because they are the direct objects of запекали.

With inanimate plural nouns, the accusative is usually the same as the nominative:

• баклажаны — nominative plural

• баклажаны — accusative plural

• кабачки — nominative plural
• кабачки — accusative plural

Because eggplants and zucchini are inanimate, the forms do not change.

So:

• запекали что? — what were we roasting?
• баклажаны, кабачки...

Because кукуруза is singular here, and it is in the accusative singular:

• nominative: кукуруза
• accusative: кукурузу

This is very normal in Russian. The speaker may be thinking of corn as a food item or ingredient in a more general/mass sense, while баклажаны and кабачки are thought of as individual vegetables in the plural.

English does something similar sometimes:

• We roasted eggplants, zucchini, and corn

Here corn is often treated like a mass noun in English too.

So the mismatch is not strange: Russian is just packaging the items slightly differently.

It is the prepositional case.

Here на means on, describing location:

• на противне — on a baking tray

Since this is a location use of на, Russian uses the prepositional case:

• большой противень — a large baking tray
• на большом противне — on a large baking tray

So both words change:

• большой → большом
• противень → противне

It looks a little unusual, but it follows a common pattern for masculine nouns ending in -ь.

противень is a masculine noun. In the prepositional singular, it becomes:

• противень → о противне / на противне

This is similar to other masculine soft-sign nouns:

• словарь → в словаре
• учитель → об учителе

So на большом противне is grammatically normal, even if the dictionary form противень makes the change feel less obvious at first.

Противень usually means a baking tray, sheet pan, or oven tray.

It is specifically the flat or shallow metal tray you put in the oven.
So in this sentence, на большом противне is something like:

• on a large baking tray
• on a large sheet pan

It is not the best word for a deep frying pan or saucepan.

Yes. Russian word order is flexible.

This sentence is natural as written:

На ужин мы запекали баклажаны, кабачки и кукурузу на большом противне.

But you could also say:

• Мы запекали на ужин баклажаны, кабачки и кукурузу на большом противне.
• Мы на большом противне запекали баклажаны, кабачки и кукурузу.
• Баклажаны, кабачки и кукурузу мы запекали на ужин на большом противне.

The basic meaning stays the same, but the emphasis shifts:

• sentence-initial На ужин highlights the meal context
• sentence-initial Баклажаны, кабачки и кукурузу highlights the food items
• moving на большом противне earlier can highlight the cooking setup

Because it works naturally as extra information about how/where the vegetables were cooked.

A very common Russian pattern is:

• time/purpose first: На ужин
• subject: мы
• action: запекали
• objects: баклажаны, кабачки и кукурузу
• location/instrument-like detail last: на большом противне

So the sentence flows from what this was for, to who did it, to what they cooked, and finally where/how it was cooked.

That final position sounds natural and unforced in Russian.

Either can work, depending on context.

The verb запекать / запечь means cooking something in the oven, often until it browns or softens. In English, that may be translated as:

• bake
• roast

With vegetables like баклажаны, кабачки и кукуруза, English often prefers roasted.
But baked is not impossible.

So запекали does not map perfectly to one single English verb in every context.