She brushed him off coldly.

Literal

She [topic-は] him [object-を] curtly handled-dismissively.

あしらう is a verb without a clean English equivalent — it means 'to handle, deal with, treat,' but specifically with a connotation of doing so dismissively, perfunctorily, or skilfully fending someone off. Pairing it with 素っ気なく ('curtly, brusquely' — adverbial form of 素っ気ない) intensifies the cold-shoulder feeling: she didn't merely engage with him minimally, she actively brushed him aside. Both words are commonly written in kana even though kanji exist, and they cluster naturally when discussing interpersonal coldness.