니 떠오르다

that reminds me of something

-(으)니 means "now that you say it / now that we're doing it," and 떠오르다 is a memory floating up on its own. Every line here is a bracketed on-screen note marking the instant a story comes back to someone: [지석이 하니 떠오른 에피소드], [여행 얘기하니 떠오름], [NG하니 떠오른 에피소드], [옛날 얘기하다 보니 떠오른 하나]. It is editor caption language rather than something people say out loud, and it works as a signpost that an anecdote is coming.

Register: on-screen caption text