Learn Hardcore Chinese: Tā yuè hē niúnǎi yuè xiǎng shuìjiào. - The more milk she drinks, the sleepier she gets.

Here: subject = 她; first clause = 越喝牛奶; second clause = 越想睡觉.
Both halves share the same subject and each half starts with 越.
Template: [Subject] 越 + verb/adjective (+ object)，(就) 越 + verb/adjective (+ object).

Where does the subject go? Can I move it?

Most commonly the subject appears once before the first 越: 她越喝牛奶，越想睡觉.

You can omit the subject if it’s obvious from context: 越喝牛奶，越想睡觉.
If you front the first 越-clause, keep the subject before the second half: 越喝牛奶，她就越想睡觉.
Repeating the subject in both halves is possible but usually unnecessary.

Do I need a comma or 就 between the two parts?

A comma is optional but common: 她越喝牛奶，越想睡觉。 Use it if the clauses are long.
就 is optional: 她越喝牛奶，就越想睡觉。 It adds a slight “then/so” feel, common in speech. Both versions are correct.

Why isn’t 了 used anywhere?

越…越… describes a tendency/correlation, not a completed event. Using 了 would shift focus to a specific occurrence. For a single event you’d say: 她喝了牛奶就想睡觉 (“after she drank milk, she wanted to sleep”), which is not the same pattern.

Why 想睡觉 and not 困? Are both okay?

Both are fine but slightly different:

想睡觉 = “feel like/want to sleep” (desire/urge).
困 = “sleepy/drowsy” (physical state).
So you can also say: 她越喝牛奶越困 (more concise, very natural).

Can I use 要 instead of 想 (i.e., 越想/越要)?

Prefer 想 here. 要 often means “intend/need to/insist on,” so 越要睡觉 can sound like determination/necessity rather than growing desire. 越想睡觉 is the neutral, natural choice.

Why is there no measure word with 牛奶? Should it be 一杯牛奶?

No measure word is needed because it’s a general statement about milk as a mass noun. If you want to quantify, restructure:

她喝的牛奶越多，就越想睡觉。
她牛奶喝得越多，就越想睡觉。 Using a specific unit (e.g., 一杯) inside the 越…越… frame is less natural unless you have a special context.

Can I shorten it to 越喝越想睡觉?

Yes, if the thing being drunk is clear from context. You can also front the topic for clarity:

她喝牛奶，越喝越想睡觉。 Without context, the bare 越喝越想睡觉 leaves “drink what?” unspecified.

Is 越来越 the same as 越…越…?

No.

越来越 + adj/VP = one thing changing over time: 她越来越想睡觉 (“she’s getting sleepier and sleepier”).
越…越… = correlation between two factors: 她越喝牛奶，越想睡觉 (“the more she drinks milk, the more she wants to sleep”).

Can I move the object before the verb, like 牛奶越喝越想睡觉?

That sounds awkward. Use one of these instead:

越喝牛奶，她就越想睡觉。
牛奶喝得越多，她就越想睡觉。
她喝的牛奶越多，就越想睡觉。

How do I make a negative like “the more…, the less…”?

Use 不 or other negatives in the second half:

她越喝牛奶，越不想睡觉。 (less willing to sleep)
她越喝牛奶，越睡不着。 (more unable to fall asleep) You can also negate the first half when appropriate.

Is 睡觉 a separable verb? Anything to watch for?

Yes, 睡觉 is a verb–object compound. In this sentence it stays together: 想睡觉. It can separate in other constructions:

睡了一觉 (slept for a while)
睡个好觉 (have a good sleep) But don’t say 想睡个觉 unless you mean “feel like taking a nap/some sleep.”

Pronunciation tips for the whole sentence?

她 tā (1st), 越 yuè (4th), 喝 hē (1st), 牛奶 niúnǎi (2nd + 3rd), 越 yuè (4th), 想 xiǎng (3rd), 睡觉 shuìjiào (4th + 4th).
Natural pause after the first clause: 她越喝牛奶，| 越想睡觉。

Can I use 愈 instead of 越?

Yes, 愈…愈… (pronounced yù) is a more formal/literary variant: 她愈喝牛奶，愈想睡觉。 In everyday speech and writing, 越…越… is more common.