01 - Whisk eggs with milk, salt, and pepper in a mixing bowl until fully combined.
02 - Heat a nonstick skillet over medium heat. Add butter or olive oil, then pour in the egg mixture. Stir gently until eggs are just scrambled and lightly set, then remove from heat.
03 - Lay the flour tortilla flat on a cutting board. Sprinkle half of the shredded cheese over one side. Top with scrambled eggs, chosen vegetable fillings, and remaining cheese. Fold the tortilla in half, pressing lightly to enclose the filling.
04 - Wipe out the skillet if necessary, return to medium heat, and place the folded quesadilla in the pan. Cook for 1 to 2 minutes per side, pressing gently, until golden brown and cheese has fully melted.
05 - Remove quesadilla from skillet. Slice into wedges with a sharp knife and serve immediately.