По мере того как вафли остывали, джем становился гуще.

It means as, as... gradually, or in proportion as.

So По мере того как вафли остывали, джем становился гуще describes two changes happening alongside each other:

• the waffles were cooling
• the jam was getting thicker

This expression is especially useful when both things change gradually over time.

They are related, but not the same.

• когда = when
  • mainly places one event in time
• пока = while / as long as
  • shows two things happening at the same time
• по мере того как = as / in proportion as
  • emphasizes that one process develops together with another

So this sentence is not just saying the waffles cooled while the jam thickened. It is saying the jam became thicker as the waffles cooled more and more.

For a learner, the easiest answer is: по мере того как is a fixed conjunction, and you should learn it as one whole unit.

You do not usually need to translate each part separately in normal use. The whole phrase means something like:

• as
• to the extent that
• in proportion as

So it is best to recognize по мере того как as one set expression.

Because вафли means waffles and it is the subject of остывали.

Here is the grammar:

• вафли = nominative plural
• остывали = past tense, plural

The verb agrees with the subject, so since вафли is plural, the verb is plural too.

If it were singular, you would get:

• вафля остывала = the waffle was cooling

Because the sentence describes a process, not a single completed event.

• остывать = to cool down, to be cooling down
• остывали = were cooling / cooled gradually

The imperfective is the natural choice here because the cooling is unfolding over time, and the jam is changing at the same time.

If you used a perfective form such as остыли, the meaning would shift more toward a completed result:

• Когда вафли остыли, джем стал гуще = When the waffles had cooled, the jam became thicker

That version sounds more like one completed stage followed by another, not two parallel gradual processes.

Становился is the past tense of становиться.

Breakdown:

• становиться = to become
• становился = was becoming / became gradually

It is:

• past tense
• singular
• masculine

It is singular masculine because the subject is джем, and джем is a masculine singular noun.

So:

• джем становился = the jam was becoming

For the same reason as остывали: the sentence describes an ongoing, gradual change.

• становился гуще = was becoming thicker
• not a sudden one-time switch, but a gradual process

This matches the meaning of по мере того как, which naturally goes with processes developing over time.

If you used perfective стал, it would sound more like a single resulting change:

• джем стал гуще = the jam became thicker

That can be correct in other contexts, but here the imperfective становился fits the gradual parallel development better.

Гуще is the comparative form of густой, which means thick.

So:

• густой = thick
• гуще = thicker

After становиться, Russian often uses a comparative to show gradual change:

• становиться гуще = to become thicker

So джем становился гуще literally means the jam was becoming thicker.

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

• становился густым = was becoming thick
  • focuses on reaching the quality thick
• становился гуще = was becoming thicker
  • focuses on a change in degree

In this sentence, the comparative гуще is better because the idea is gradual increase: the longer things went on, the thicker the jam got.

So гуще matches the logic of по мере того как very well.

Yes. Джем густел is also possible and natural.

Compare:

• джем густел = the jam was thickening
• джем становился гуще = the jam was becoming thicker

The meaning is very close. The version with становился гуще is a bit more explicit about the comparison and the gradual change in thickness.

Because the sentence begins with a subordinate clause:

• По мере того как вафли остывали = subordinate clause
• джем становился гуще = main clause

Russian separates them with a comma.

Also, there is no comma inside по мере того как here, because it is functioning as one conjunction.

Yes. Russian can put the main clause first or second.

For example:

• По мере того как вафли остывали, джем становился гуще.
• Джем становился гуще по мере того как вафли остывали.

Both mean essentially the same thing.

Putting По мере того как вафли остывали first gives a natural setup: first the changing condition, then the result that develops alongside it.