Prepare the eggs
In a mixing bowl, whisk together eggs, milk, salt, and pepper until well combined.
Cook the eggs
Heat 1 tablespoon of butter in a skillet over medium heat. Pour in the egg mixture and gently scramble until just set. Remove from heat and set aside.
Assemble the quesadillas
Lay a tortilla flat on a clean surface. Sprinkle half of the cheese on one side of the tortilla, followed by scrambled eggs, bacon or sausage, bell peppers, and green onions. Add the remaining cheese on top and fold the tortilla in half.
Cook the quesadillas
Heat the remaining butter in a skillet over medium heat. Place the folded quesadilla in the skillet and cook for 2-3 minutes on each side, or until golden brown and the cheese is melted. Repeat with the remaining tortillas.
Slice and serve
Remove the quesadillas from the skillet and let cool slightly. Cut into wedges and serve warm.