Preheat oven to 250°F.
Spread butter on one side of each tortilla. Place tortillas, one at a time, butter-side down in large skillet or griddle over medium heat. Add about 3 tablespoons cheese and fold tortillas in half over filling, so buttered side is out.
Toast folded tortillas until golden – about 1 minute per side. Work in batches and transfer cooked tortillas to a baking pan in preheated oven.
Use a pizza wheel to cut each folded tortilla into halves. Serve with salsa.
Yields 32 pieces, so could serve 16 as appetizer or 8 as entrée.