In a mixing bowl, whisk the eggs with milk or cream, salt, and pepper.
Heat a lightly oiled or buttered skillet over medium heat.
Pour the egg mixture into the skillet and cook, stirring occasionally, until the eggs are set but still slightly moist. Remove from skillet and set aside.
Lay one tortilla flat on a clean surface. Sprinkle half of the shredded cheese evenly over the tortilla.
Top with the cooked eggs, cooked meat (if using), and vegetables (if using).
Sprinkle the remaining cheese over the fillings.
Top with the second tortilla.
Carefully transfer the quesadilla to the heated skillet. Cook for 2-3 minutes per side, or until the tortilla is golden brown and the cheese is melted and gooey.
Remove the quesadilla from the skillet and let it cool slightly.
Cut the quesadilla into wedges. Serve immediately with your favorite toppings, such as salsa, sour cream, or guacamole.