01 - In a small bowl, whisk eggs with milk or cream, salt, black pepper, and smoked paprika until thoroughly blended.
02 - Heat a nonstick skillet over medium heat and add butter. Sauté red bell pepper and green onion until softened, about 2 minutes.
03 - Add egg mixture to the skillet with vegetables and gently scramble until eggs are softly set, 2 to 3 minutes. Remove skillet from heat and set aside.
04 - Lay one tortilla flat on a clean work surface. Distribute half of the cheddar and Monterey Jack cheese evenly over the surface, then add scrambled eggs, chicken, and sautéed vegetables. Top with remaining cheese.
05 - Place second tortilla over the filling to cover completely.
06 - Heat a large skillet or griddle over medium heat. Carefully slide assembled quesadilla into the pan. Cook for 2 to 3 minutes per side, pressing gently with a spatula, until both sides are golden brown and crisp and the cheese is melted.
07 - Remove quesadilla from heat. Let rest for 1 to 2 minutes, then slice into wedges and serve immediately.