sachoni chucheonhan jakga inteobyureul bogo nanikka geu soseoreul ilggo sipeojyeosseo.

It is a relative clause that modifies the noun that follows it.

• 추천하다 = to recommend
• 추천한 = recommended / that (someone) recommended

So:

• 사촌이 추천한 작가 인터뷰 = the author interview that my cousin recommended

Here, 사촌이 is the subject inside that mini-clause:

• 사촌이 추천하다 = my cousin recommends/recommended

In Korean, relative clauses come before the noun they describe, unlike English.

Because 사촌 is the subject of 추천한.

• 이/가 marks the subject
• 을/를 marks the object

So:

• 사촌이 추천한 = that my cousin recommended
• 사촌을 추천한 would mean that recommended my cousin or involve my cousin as the object, which is not the meaning here

Your cousin is the one doing the recommending, so 이 is correct.

In this sentence, 작가 인터뷰 most naturally means an interview with the author.

Korean noun compounds can be a little flexible, but in everyday usage:

• 작가 인터뷰 usually means an author interview / an interview featuring the author

If you wanted to clearly say an interview the author conducted, Korean would usually express that more explicitly, such as with a longer phrase.

So here, the natural reading is:

• the interview with the author that my cousin recommended

를 marks 작가 인터뷰 as the object of 보다.

• 작가 인터뷰를 보다 = to watch / see / read the author interview

So the structure is:

• [작가 인터뷰를] 보고 = after watching/seeing/reading [the author interview]

보다 is very broad in Korean. It can mean:

• to see
• to watch
• to look at
• sometimes even to read, depending on the thing being viewed

With 인터뷰, the exact English translation depends on context:

• if it was a video interview: watched
• if it was a written interview: read
• if the context is unclear: saw is often safest

So 작가 인터뷰를 보고 could reasonably be translated as:

• after watching the author interview
• after seeing the author interview
• after reading the author interview

-고 나니까 means something like:

• after doing...
• once I did...
• after I did it, I realized/felt...

It often emphasizes a result or change noticed afterward.

So:

• 보고 나니까 그 소설을 읽고 싶어졌어 = after seeing the interview, I came to want to read that novel = once I saw the interview, I wanted to read that novel

Compared with -고 나서, -고 나니까 more strongly suggests that something became clear or changed as a result.

Both can mean after doing something, but there is a nuance difference.

• -고 나서: more neutral sequence
  
  • after doing X, then Y
• -고 나니까: often suggests a result, realization, or new state after X
  
  • after doing X, I found that Y / I ended up feeling Y

In this sentence, 나니까 fits well because the speaker’s desire changed:

• after seeing the interview, they started wanting to read the novel

So 보고 나서 읽고 싶었어 is possible, but 보고 나니까 읽고 싶어졌어 more clearly shows a new feeling arising after the experience.

This is an important nuance.

• 읽고 싶었어 = I wanted to read it
• 읽고 싶어졌어 = I came to want to read it / I started wanting to read it

The form -아/어지다 means to become.

So:

• 싶다 = to want
• 싶어지다 = to come to want / to start wanting

This sentence is describing a change in feeling:

• before seeing the interview, maybe the speaker did not especially want to read the novel
• after seeing it, that desire appeared

That is why 싶어졌어 is especially natural here.

-고 싶다 attaches to a verb stem and means want to do that action.

Examples:

• 읽고 싶다 = want to read
• 먹고 싶다 = want to eat
• 가고 싶다 = want to go

So in this sentence:

• 그 소설을 읽고 싶어졌어 = I came to want to read that novel

A useful thing to remember: -고 싶다 is normally used for the speaker’s own desire, or in questions about the listener’s desire.

Because 그 소설 is the object of 읽다.

• 그 소설을 읽다 = to read that novel

So:

• 을/를 marks what is being read

If you used 그 소설이, that would make the novel the subject, which would not fit 읽다 here.

It is omitted, which is very common in Korean.

The full idea is something like:

• (나는) 사촌이 추천한 작가 인터뷰를 보고 나니까 그 소설을 읽고 싶어졌어.

Korean often leaves out subjects when they are obvious from context. In this sentence, the final verb 싶어졌어 strongly suggests the speaker’s own feeling, so I is naturally understood.

It is casual/informal speech.

The ending -어졌어 is the informal style often used with friends, family, or people you are close to.

A more polite version would be:

• 사촌이 추천한 작가 인터뷰를 보고 나니까 그 소설을 읽고 싶어졌어요.

Same meaning, but more polite.

Grammatically, Korean relative clauses modify the noun phrase that follows, so learners sometimes wonder about the scope. In this sentence, the natural interpretation is:

• [사촌이 추천한] [작가 인터뷰] = the author interview that my cousin recommended

not:

• the author whom my cousin recommended + interview

That second reading would be odd in context, because 작가 인터뷰를 보다 is a very natural unit: to watch/read an author interview.

So the phrase is best understood as one chunk:

• the author interview my cousin recommended

Yes, that is the most natural implication.

The sentence says:

• the speaker saw an interview with an author
• then wanted to read that novel

In context, 그 소설 most likely refers to a novel by that author, or a novel being discussed in the interview.

However, grammatically, the sentence itself does not explicitly say the author’s novel. That connection comes from context and common sense.

Yes, that is a good natural translation.

If you want to capture the nuance of 싶어졌어 more closely, these are even better:

• After seeing the author interview my cousin recommended, I started wanting to read that novel.
• After watching the author interview my cousin recommended, I came to want to read that novel.
• Once I saw the author interview my cousin recommended, I wanted to read that novel.

The key nuance is that the desire arose as a result of seeing the interview.