Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease. Let sausage cool.

Spray a large skillet with cooking spray; warm over medium-high heat. Beat eggs with milk in a bowl. Pour into the skillet; cook and stir until eggs are set, about 5 minutes. Set aside to cool.

Spread butter over 1 side of each tortilla. Heat a skillet over medium heat. Place a tortilla, buttered-side down, in the skillet. Top with a layer each of the sausage, eggs, then cheese. Top with another tortilla, buttered-side up. Cook until golden brown on both sides, 2 to 3 minutes per side. Transfer to a plate. Repeat with remaining tortillas and filling.

Slice quesadillas into quarters. Serve.