Learn Hardcore Korean: gamgiga ppalli naasseumyeon johgessda.

It’s a set pattern meaning I wish/hope (that) X were the case. The -았/었- here doesn’t mark real past time; it often expresses the desired result state as if it had already happened. With verbs that describe reaching a state (recover, finish, be over), Koreans commonly prefer -았/었으면 좋겠다 to sound like I wish it were already done. So 감기가 빨리 나았으면 좋겠다 ≈ I hope my cold gets better soon (I wish it were already gone).

Why is it 나았으면 and not 낫으면?

Because 낫다 (to get better/recover) is a ㅅ-irregular verb. The ㅅ in the stem drops before a vowel.

Stem: 낫-
- -았으면 → 나았으면 Other common forms: 나아요, 나았어요, 나을 거예요.

Why 감기가, not 감기를?

With 낫다, the illness is treated as the grammatical subject in Korean. You say 감기가 낫다 (the cold is cured), not 감기를 낫다. Similar patterns:

머리가 아프다 (my head hurts)
열이 나다 (I have a fever)

Can I say 나으면 좋겠다 instead of 나았으면 좋겠다?

Yes, but there’s a nuance difference.

나으면 좋겠다: a general hope (If it gets better, that would be good).
나았으면 좋겠다: wishful desire for the already-achieved result state (I wish it were already better). For recovery, the -았으면 version is more idiomatic and common.

Where is the I in this sentence? How do I show whose cold it is?

Korean often omits obvious pronouns. 좋겠다 implies the speaker’s viewpoint: I hope. Whose cold it is is understood from context. To be explicit:

My cold: 제 감기가 빨리 나았으면 좋겠어요.
Your cold (casual): 네 감기가 빨리 나았으면 좋겠어.
Someone named: 민수 씨 감기가 빨리 나았으면 좋겠어요.

What politeness or honorific options do I have?

Plain: … 좋겠다.
Polite: … 좋겠어요.
Formal: … 좋겠습니다. If you’re wishing recovery for a respected person, either drop the illness subject and honorify the verb:
빨리 나으셨으면 좋겠어요/좋겠습니다. Or keep the noun and show respect via the possessor:
선생님 감기가 빨리 나았으면 좋겠어요.

Can I move 빨리? Are there alternatives?

Yes. 감기가 빨리 나았으면 좋겠다, 빨리 감기가 나았으면 좋겠다, and 감기가 나았으면 빨리 좋겠다 (awkward) aren’t equally natural; the first two are fine, with the first most common. Alternatives to 빨리: 얼른, 어서 (both very natural in this context). 빠르게 is more formal/technical and less natural here.

What’s the difference between 낫다, 나아지다, and 회복하다?

낫다: to recover/be cured (most idiomatic with illnesses like colds). Example: 감기가 다 나았어요.
나아지다: to improve (symptoms/condition). Example: 증상이 많이 나아졌어요.
회복하다: to recover (more formal/overall recovery). Example: 건강을 회복했어요.

Does -으면 좋겠다 ever make a suggestion?

Yes, it can be a soft suggestion or wish about someone else’s action:

약을 드셨으면 좋겠어요. (I’d like you to take medicine / You should take medicine.) It’s gentler than commands, but context and intonation matter to keep it polite.

Why not use the topic marker -는: 감기는 빨리 나았으면 좋겠다?

You can. 감기는 topicalizes the cold (as for the cold, I hope it gets better soon), which can sound a touch more contrastive or framing. 감기가 simply marks it as the grammatical subject. Both are acceptable; 감기가 is the neutral default here.

How is 좋겠다 different when used by itself, like 좋겠다!?

Standalone 좋겠다! often expresses envy or conjecture (That must be nice / Lucky you!). In the pattern -으면 좋겠다, it expresses a wish/hope. So:

휴가라서 좋겠다! (Lucky you, you’re on vacation!)
휴가가 있었으면 좋겠다. (I wish I had a vacation.)

Pronunciation tip: how do I say 나았으면 smoothly?

It’s pronounced as if 나아쓰면: the hiatus 나아- is clear, and the ㅆ links to the following syllable. Saying it slowly as 나-아-쓰-면 helps, then speed up.

Is 빨리 낫고 싶다 okay? How does it differ from … 나았으면 좋겠다?

Both are fine:

빨리 낫고 싶다: a direct personal desire (I want to get better soon).
빨리 나았으면 좋겠다: a softer, wishful hope (I hope I’m better soon). The latter sounds less self-centered and is very common in everyday speech.

How would I say I wish it hadn’t gotten worse / I hope it doesn’t get worse?

Regret about past worsening: 더 나빠지지 않았으면 좋았을 텐데. (I wish it hadn’t gotten worse.)
Hope about the future: 더 나빠지지 않았으면 좋겠다 or 더 나빠지지 않으면 좋겠다. Both are used; the -았으면 version frames the desired ongoing state as not having worsened.