Here's some grammar-related information. 1 매일 그린 그림이 바로 당신이란 걸: That the drawing I drew everyday is of you. (이란 걸 = 이라는 것을) 2 아무 이유도 없이 보고 싶었다는 걸: That I missed you with no particular reason at all. (싶었다는 걸 = 싶었다는 것을) These are elliptical sentences with the main verb omitted at the end. For example, #1 could be: 매일 그린 그림이 바로 당신이란 걸 [당신은 알까]? => [Would you know] that the drawings I drew everyday was of you? It is left for the listener how to take it, but very often it's obvious by the context. Grammatically, there is a difference between the two in terms of their verbs and quoting structure. Verbs (and adjectives which are similar) in Korean can be categorized into three groups. 1. special verb (technically a particle) 이다: matches the equating "is" in English (AA is BB), where BB is a noun. 2. special verb 있다: corresponds to "is" or "exist" in English (There is ...). 3. All other verbs. Your #1 example is using the special 이다 verb. - [매일 그린 그림]이 (바로) [당신]이다: The drawing I drew everyday is of you. - '[그림]이 [당신]이다'라는 것 (direct quoting) -> 그림이 당신이라는 것(indirect quoting): that the drawing is of you. In #2 example, it is a general verb(actually an adjective 싶었다). - 아무 이유도 없이 보고 싶었다. - '아무 이유도 없이 보고 싶었다'라는 것 (direct) -> 아무 이유도 없이 보고 싶었다는 것 (indirect). So the indirect quotation forms change between the special verb 이다 and al other others. (Direct quotes always use -라고 and -라는 after the quoted phrase regardless of the verb involved) 이다 uses -라고 (하는), -라는, and so on while all other verbs use -다고 (하는), -다는, etc. - 그는 회사 회사원이라고 한다: They say he is a company employee. (connecting IS - 이다 + 라고 -> 이라고) - 그는 어느 회사에 있다고 한다: They say he is with a company. (IS (exist) - 다고) - 그는 회사에 다닌다고 한다: They say he works at a company. (general verb - 다고) Different tenses use the different suffixes like ㅆ(있다고), ㄴ(다닌다고), on the verb stem.

You already know, These sentences are short forms. 란걸 -> 라는 것을. 걸 -> 것을. I think English also has these short forms like it. I am -> I'm You are -> You're ........

걸 = 것을 Those sentence is not completed. But they have meaning enough. "매일 그린 그림이 바로 당신이란걸" > 매일 그린 그림이 바로 당신이란 것을 (당신은 몰랐을 거야. 등) "아무 이유도 없이 보고싶었다는걸" > 아무 이유도 없이 보고싶었다는 것을 (당신은 몰랐을 거야. 등)

really for monologue with a hint of regret