Learn Hardcore Chinese: Wǒ yuè máng yuè xiǎng hē kāfēi. - The busier I am, the more I want to drink coffee.

Here, 越忙 = “the busier (I am),” and 越想喝咖啡 = “the more (I) want to drink coffee.”
So: 我越忙越想喝咖啡 = “The busier I am, the more I want to drink coffee.”

Do I have to repeat 越 twice?

Yes. In this pattern, 越 must appear before both parts: 越A 越B. Saying only one 越 (e.g., 我越忙想喝咖啡) is ungrammatical in standard Mandarin.

Where should the subject go? Can I repeat it?

Common options:

我越忙越想喝咖啡 (subject once at the start; very common)
我越忙，我越想喝咖啡 (subject repeated; adds a slight pause/emphasis)
越忙我越想喝咖啡 (fronts the condition for emphasis) You can repeat 我 in the second half or leave it implied; both are fine.

Is a comma required between the two halves?

Not required. A comma is often inserted to reflect the natural pause: 我越忙，越想喝咖啡 or 我越忙，我越想喝咖啡. Without a comma is also fine in short sentences.

Can I omit the subject entirely?

Yes, if context is clear: 越忙越想喝咖啡 can mean “The busier (one is), the more (one) wants to drink coffee.” In conversation, this is natural when the subject is obvious.

Why isn’t there 很 or 是 before 忙?

忙 is a stative adjective (verb-like in Chinese). You don’t use 是 before adjectives in predicates.
You often add 很 with adjectives in simple statements, but here 越 already functions as a degree adverb, so 很 is neither needed nor used: 越忙, not 越很忙.

What kinds of words can follow 越?

Typically adjectives or verb phrases:

After the first 越: adjectives (忙, 冷, 热) or verb phrases (学习、说中文).
After the second 越: adjectives/verbs/quantifier phrases (越开心, 越想休息, 越多/越少). Examples:
天气越冷，人越少。
你越说，我越不懂。
时间越紧任务越多。

What’s the difference between 越…越… and 越来越?

越…越… links two things: as A increases, B also changes. Example: 天气越冷，人越少 (“the colder it gets, the fewer people there are”).
越来越 + Adj./Verb describes one thing changing over time: 我越来越想喝咖啡 (“I want coffee more and more”). Your sentence is correlation (busy ⇒ want coffee), not just a single trend.

What’s the nuance difference between 想喝, 要喝, and 想要喝?

想喝: feel like/would like to drink (polite, softer desire).
要喝: want to drink/going to drink (stronger, intention or decision).
想要喝: stronger desire than 想喝; often used when emphasizing wanting something. Your sentence uses 想喝 to express increasing desire, not a firm decision.

Can I add 就 as in 我越忙就越想喝咖啡?

Yes. 就 is optional and can make the link feel a bit tighter or more natural in some contexts: 我越忙就越想喝咖啡. Meaning is essentially the same.

What if I want to say I actually drink more coffee, not just want it?

Change the second half to an action: 我越忙越喝咖啡 = “The busier I am, the more I drink coffee.”
Your original with 想喝 is about desire, not necessarily action.

How do I negate this pattern?

Negate the part you want:

Negate B: 我越忙越不想喝咖啡 (“the busier I am, the less I want to drink coffee”).
You can also negate A or use 越不…越…/越没…越… depending on meaning, e.g., 越不休息越累 (“the less you rest, the more tired you get”). Use 不 for general negation of habits/states; 没 for past/completed actions.

Can a noun follow 越 directly?

Not a bare noun. You’d use quantity/degree with it:

咖啡越多越兴奋 (“the more coffee, the more excited”).
Or restructure: 我越忙，咖啡喝得越多 (“The busier I am, the more coffee I drink”). So pair 越 with adjectives, verbs, or degree words (多/少/快/慢), not plain nouns.

Is 愈…愈… the same as 越…越…?

Yes in meaning; 愈 (yù) is a more formal/literary variant. 愈来愈 also corresponds to 越来越. In everyday speech, 越 is much more common.

Any pronunciation tips for this sentence?

越 (yuè) is 4th tone both times.
忙 (máng) 2nd, 想 (xiǎng) 3rd, 喝 (hē) 1st, 咖啡 (kāfēi) 1st + 1st.
No tricky third-tone sandhi here because 想 (3rd) is followed by 喝 (1st), not another 3rd tone.

Where do measure words go if I specify an amount, like “a cup of coffee”?

After the verb: 我越忙越想喝一杯咖啡 (“the busier I am, the more I want to drink a cup of coffee”).
You can also say 越想喝更多咖啡 to emphasize “more coffee.”

Can I swap the halves, like 越想喝咖啡越忙?

You can grammatically, but it changes the meaning to “the more (I) want to drink coffee, the busier (I) get,” which is a different (and often odd) claim. Keep the cause/condition first and the resulting change second to say what you intend: 越忙越想喝咖啡.

What about the variant 越是…越…?

越是…越… adds emphasis, often in more formal or emphatic statements: 我越是忙，越想喝咖啡. Meaning is the same; the tone is slightly stronger or more deliberate.