Когда мы печём торт, брат обычно включает миксер, а я взбиваю яйца.

Because this sentence describes a usual, repeated situation: when/whenever we bake a cake.

In Russian, the present tense of imperfective verbs is commonly used for habits and repeated actions:

• Когда мы печём торт... = When/Whenever we bake a cake...
• брат обычно включает...
• я взбиваю...

So this is not talking about one specific cake right now, but about what normally happens.

Печём is the 1st person plural present form of печь (to bake).

This verb is a little irregular, so its forms do not look exactly like the infinitive:

• печь = to bake
• я пеку = I bake
• мы печём = we bake

So мы печём means we bake.

The letter ё is important because it shows both:

• the pronunciation, and
• the stress

So печём is stressed on the last syllable: пе-чём.

In many Russian texts, ё is often written as е, so you may also see печем in ordinary writing, even though it is still pronounced печём.

Because Когда мы печём торт is a subordinate clause introduced by когда.

Russian normally separates this kind of clause with a comma:

• Когда мы печём торт, ...

This is similar to English:

• When we bake a cake, ...

Here торт is the direct object of печём, so it is in the accusative case.

But торт is:

• masculine
• inanimate

For masculine inanimate nouns, the accusative singular looks the same as the nominative singular. So:

• nominative: торт
• accusative: торт

That is why the form does not visibly change.

Russian often leaves out possessives like my, your, our when the meaning is already clear from context.

So брат here naturally means my brother or the brother relevant to the situation, depending on context. In everyday Russian, this is very common.

If you wanted to make it explicit, you could say:

• мой брат обычно включает миксер

But it is not necessary here.

Обычно means usually, and its position is quite natural here:

• брат обычно включает миксер

Russian word order is flexible, but this order sounds neutral and natural. It puts обычно close to the verb it modifies.

Other placements are possible, but they may sound more marked or emphasize something different.

А often marks a contrast or a switch of focus, even when both parts are positive.

Here the idea is:

• my brother does one part
• I do another part

So а works well because it sets the two actions side by side:

• брат обычно включает миксер, а я взбиваю яйца

If you used и, it would sound more like simple addition. А is better for as for me / while I.

Yes, Russian often omits subject pronouns when they are clear from the verb form.

So in theory, you could say:

• ...а взбиваю яйца

But here я is very natural because it adds contrast:

• brother does this, and I do that

So а я means something like:

• while I...
• and I, meanwhile...
• as for me, I...

Включает comes from включать / включить, which means to turn on, to switch on.

So:

• включает миксер = turns on the mixer

Here миксер is the direct object: the thing being turned on.

Because the sentence describes a habitual action, the imperfective verb включает is used.

Взбиваю is the imperfective present form of взбивать (to beat / whisk).

So:

• я взбиваю яйца = I beat/whisk the eggs

The imperfective is used because the sentence describes a repeated, usual activity, not one completed action on one specific occasion.

The aspect pair is:

• взбивать = imperfective
• взбить = perfective

Here the imperfective is the correct choice.

Яйца is the plural of яйцо (egg).

After взбиваю, it is the direct object, so it is in the accusative plural. But for inanimate nouns, the accusative plural often looks the same as the nominative plural.

So:

• singular: яйцо
• plural: яйца

That is why you see яйца here.

In this context, it really means whenever.

Because the verbs are in the present imperfective and the sentence describes a routine, Когда мы печём торт is understood as:

• When/Whenever we bake a cake

English often uses whenever to make the habitual meaning clearer, but Russian can use just когда for that.