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 flour mixture, shaking off excess. Dip into 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 to 350°F. Fry onion rings in batches without overcrowding, turning once, until golden brown and crispy, about 2-3 minutes per batch. 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. Arrange fried onion rings over the cheese, then drizzle with 2 tablespoons sour cream and sprinkle with chives if using.
05 - Top with a second tortilla. Cook for 2-3 minutes until the bottom tortilla is golden brown and cheese begins to melt. Carefully flip and cook an additional 2 minutes until the second side is golden and cheese is completely melted.
06 - Transfer quesadilla to a cutting board and let cool for 1 minute. Cut into 6 wedges. Serve immediately with salsa, guacamole, and additional sour cream on the side.