01 - Separate onion slices into individual rings. Combine flour, smoked paprika, garlic powder, and salt in a shallow bowl. Whisk eggs in a separate bowl. Place panko breadcrumbs in a third bowl. Dredge each onion ring in the flour mixture, shake off excess, dip into the beaten eggs, then coat thoroughly with panko breadcrumbs, pressing gently to adhere.
02 - Pour vegetable oil into a deep skillet to a depth of 2 inches and heat over medium-high heat until it reaches 350°F. Fry onion rings in batches, being careful not to overcrowd the pan, until golden brown and crispy, approximately 2-3 minutes per batch. Transfer to a wire rack or paper towels to drain excess oil.
03 - Heat a non-stick skillet over medium heat. Place one tortilla in the skillet and evenly distribute one-quarter of the cheddar and mozzarella cheeses over the surface. Arrange several fried onion rings over the cheese layer, then drizzle with 2 tablespoons of sour cream. Sprinkle with fresh chives if desired. Top with a second tortilla.
04 - Cook for 2-3 minutes until the bottom tortilla is golden brown and the cheese begins to melt. Carefully flip using a large spatula and cook for an additional 2 minutes until the second side is golden and the cheese is completely melted. Transfer to a cutting board and let rest for 1 minute before slicing.
05 - Cut each quesadilla into 6-8 wedges using a sharp knife or pizza cutter. Arrange on a serving platter and serve immediately with salsa, guacamole, and additional sour cream on the side for dipping.