At the bottom of this picture it says あーんしちゃろうか？
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At first I also thought it might be 「してしまう」 but only something very unhealthy (i.e. a guilty pleasure) would justify this. The 高菜チャーハン (たかなちゃあはん) seemed pretty healthy to me.
On further examination (and checking with a native speaker) we concluded it's して + やろうか
The ちゃ sound results from mixing the て+や very quickly into しちゃ.
Here's an example from the wild: 「。。。おか〜ちゃんがダッコしちゃろうか（ダッコしてやろうか）」
Ref: http://koryu04.exblog.jp/7853917/ + bonus material, this page has pictures of puppies!