The bright lights of the Waffle House off Tucson’s Grant and I-10 pierce the night at 2 a.m. like a kind of comforting beacon to all who may enter. Inside, the quiet hum of the lighting feels almost like a church-like quietness, punctuated only by the scripture of the cook’s spatula on the grill and the crackling noise of eggs frying on the skillet.

As it basks in the light of international recognition, Tucson has upped its game in the culinary world. Being labeled North America's first “City of Gastronomy” by UNESCO in December...