Heat oil over medium heat; then add shallot and garlic.
Cook, stirring frequently, until shallot is tender, about 5 minutes. Add beans, salt, and chili powder; mash with back of spoon or potato masher to make a pulpy mixture. Remove from heat; set aside.
Place tortilla chops on a timed baking sheet. Spoon bean mixture over top and sprinkle with cheese. Bake until cheese melts, about 3 minutes. Remove from oven and spoon salsa over top; immediately sprinkle with cilantro. Yields 5 topped chips per serving.