。
She's nosy, but I still like her.
Literal
She [topic-は] prying-fond is [although-けれども], I [topic-は] her [subject-が] liked.
詮索好き (せんさくずき) literally 'fond of prying' — combining 詮索 ('inquiry / probing') with the suffix ~好き ('fond of, lover of'). The ~好き suffix is productive: お酒好き ('a fan of drinking'), 子供好き ('fond of children'), 世話好き ('caring / fond of looking after others'). The pattern ではあるけれども concedes a point: では (= でも + は contracted, 'as for being X') + ある (copula 'to be') + けれども ('but') makes 'while it is true that X, ...'. The second clause uses XはYが好きだ — the canonical Japanese double-particle pattern for liking, where the liker is the topic and the liked thing takes が.