。
She gave me a lovely smile.
Literal
She [topic-は] me [to-に] lovely smile [object-を] cast [for me-てくれた].
微笑みを投げかける ('to cast a smile') is a slightly literary collocation, where 投げかける ('throw at, cast toward') extends the metaphor of a smile as a thing flung outward. 投げかける is a productive compound: 影を投げかける ('cast a shadow'), 視線を投げかける ('cast a glance'), 質問を投げかける ('throw out a question'). The act-as-thrown-thing metaphor works for any directed action. 微笑み — the noun form of 微笑む ('smile gently') — is the warmer, more visual cousin of 笑顔 ('smiling face').