"새삼 말하기도" == "새삼스레 말하기도 / 새삼스럽게 말하기도" ( it has nothing to do with the plant :-)
새삼, 새삼스레, and 새삼스럽게 mean "all over again", "anew", "afresh", or "over again as if it is new", etc.
It is a common word in Korean but English seems to have no exact matching word.
새삼스럽다, 새삼스러운, and 새삼스런 are its adjective forms.
Examples will help you understand it.
- 지난날들이 새삼 그립다: I miss the old times all over again.
- 나는 그의 말솜씨에 새삼 놀랐다: I was surprised yet again at his glibness.
- 그 문제를 왜 새삼 끄집어내냐?: Why are you bringing up that issue now for no reason?
- 몇 년 만에 보는 고향 산천이 새삼스럽다: The countryside of home looks rather different after all these years.
- 새삼스레 무슨 존댓말을 쓰냐: Why are you using honorifics with me all of a sudden?
- 새삼 말하기도 민망하지만 이대로 좋구나: It's a bit awkward to mention it afresh, but I sure like it as it is now.
AA: 항상 이렇게 도와 주셔서 감사합니다: I thank you for all the things you've done for me.
BB: 새삼(스럽게) 무슨 그런 말씀을 하세요? Please don't say such a thing as if we are new to each other or something.