In a bowl, whisk together 2 eggs and 1½ tablespoons milk until smooth.
Melt 1 teaspoon butter in a 6-inch skillet over medium heat.
Add the diced bell pepper and onion. Cook for about 5 minutes or until the onion becomes translucent.
Remove half of the vegetable mixture and set it aside for the second quesadilla.
Pour the egg mixture into the skillet with the remaining vegetables.
As the eggs begin to cook, gently lift the cooked edges and tilt the pan so uncooked egg flows underneath. Continue until the eggs are mostly set.
Cook for about 2 minutes, then carefully flip the omelet and cook for another 1 to 2 minutes until lightly golden.
Slide the omelet onto one tortilla.
Place the tortilla back into the skillet, top the omelet with one cheese slice, and cover with a second tortilla.
Cook until the bottom tortilla is golden brown, about 2 minutes.
Carefully flip and cook the other side for about 1 minute.
Transfer to a cutting board and slice into quarters.
Repeat the process with the remaining eggs, milk, vegetables, cheese, butter, and tortillas to make the second Egg and Cheese Breakfast Quesadillas batch.
Serve warm and enjoy.