Use a table knife to spread half of the refried beans on 1 tortilla.
Place bean-topped tortilla in a medium skillet or griddle with the bean side up. Put skillet on a burner. Turn the burner to medium heat. Sprinkle half of the cheese over tortilla. Top with 1 plain tortilla.
Cook over medium heat about 3 minutes or until cheese begins to melt. Use a pancake turner to turn quesadilla over. Cook 2 minutes more. Use pancake turner to remove quesadilla from skillet. Repeat with remaining tortillas, refried beans, and cheese. Turn off burner. Remove skillet from burner. Use pancake turner to remove quesadilla from skillet.
Use scissors to cut each quesadilla into 4 triangles. Serve with salsa, if you like. Makes 4 servings.