01 - Separate onion slices into individual rings. Set up three shallow bowls: mix flour, smoked paprika, garlic powder, and salt in the first; whisk eggs in the second; place panko breadcrumbs in the third.
02 - Dredge each onion ring in the seasoned flour mixture, shaking off excess. Dip into the beaten eggs, allowing excess to drip off. Press firmly into panko breadcrumbs to coat evenly on all sides.
03 - Heat 2 inches of vegetable oil in a deep skillet over medium-high heat until it reaches 375°F. Fry onion rings in batches without overcrowding, cooking 2-3 minutes until golden brown and crispy. Transfer to a wire rack or paper towels to drain.
04 - Heat a non-stick skillet over medium heat. Place one tortilla in the pan. Sprinkle evenly with 1/2 cup cheddar and 1/4 cup mozzarella cheese, covering the tortilla surface.
05 - Arrange fried onion rings evenly over the cheese. Drizzle with 2 tablespoons sour cream and sprinkle with 1/2 tablespoon chives if using. Place a second tortilla on top to create a sandwich.
06 - Cook for 2-3 minutes until the bottom tortilla is golden brown and cheese begins to melt. Carefully flip using a large spatula and cook another 2 minutes until the second side is golden and cheese is completely melted. Transfer to a cutting board.
07 - Let quesadilla rest for 1 minute, then cut into 6 wedges. Serve immediately with salsa, guacamole, and additional sour cream on the side. Repeat with remaining ingredients to make 4 quesadillas total.