Caramelized Onion and Jalapeño Quesadillas

Melt butter in a large skillet over medium-low heat. Add onion; cook and stir until softened and lightly browned, about 10 minutes. Add jalapeño peppers; cook and stir until onion is browned, about 10 more minutes. Transfer mixture to a plate.

Heat about 1 tablespoon oil in the same skillet. Add one tortilla; top with 1/4 cup cheese, 1/2 of the onion mixture, and another 1/4 cup cheese. Top with another tortilla and cook quesadilla until browned and cheese is melted, 1 to 2 minutes per side. Remove to a plate, add more oil to the skillet, and repeat to make remaining quesadilla.