Staten Island, long ignored by New York City’s foodies, is developing a restaurant scene more similar to the other boroughs, complete with food halls, taco arcades and two-hour waits for brunch.

Mighty Quinn’s, a “New York-style barbecue” chain, is opening its first restaurant on Staten Island next year as part of Empire Outlets, a 350,000-square-foot shopping complex under construction near the ferry terminal. Two Boots, the Cajun-flavored pizza chain, will also be part of the project with its first Staten Island foray, as...