01 - Separate onion slices into individual rings. Set up three shallow bowls: combine 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 total. Transfer to paper towel-lined plate to drain.
04 - Heat a large 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.
05 - Arrange fried onion rings over the cheese layer. Drizzle with 2 tablespoons sour cream and sprinkle with 1/2 tablespoon chives if using. Place second tortilla on top.
06 - Cook for 2-3 minutes until bottom tortilla is golden brown and cheese begins to melt. Carefully flip with spatula and cook additional 2 minutes until second side is golden and cheese is completely melted. Transfer to 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.