、。
She kindly asked, "Are you all right?"
Literal
She [topic-は] very kindly, all-right is [quotative-と] asked.
優しく is the adverbial form of the i-adjective 優しい (kind/gentle), produced by swapping the final い for く — here it functions as a conjunctive adverb attaching the manner of the action ('kindly') to the verb. The と after 大丈夫ですか is the quotative particle, marking direct quotation: the speech is preserved word-for-word, including its polite ですか. 聞く is the workhorse verb for both 'ask' and 'listen' — context disambiguates.