Why is the imperative used (...ke mi manĝu...)?
Because it's a "desired result" - you would also use it after "want, desire, wish" and similar verbs.
Note that conservative English grammar would use the subjunctive here: "What do you recommend that he eat in the restaurant?" (rather than that he eats, indicative).
Esperanto doesn't have an imperative mood or subjunctive mood, but what's called a 'jussive' mood that talks about requests, wishes, desires, &c. This is used in cases where languages would use the imperative mood or subjunctive mood.
Seems like it should take suggest in place of recommend. I reported that.
Suggest and recommend are not exactly the same