01 - Peel onions and slice crosswise into 1/2-inch thick rings. Carefully separate into individual rings. Reserve the largest, most intact rings for stuffing. Set aside until ready to use.
02 - Arrange three shallow bowls in assembly line fashion. Place flour in the first bowl. Beat eggs in the second bowl. Combine panko breadcrumbs, smoked paprika, garlic powder, salt, and pepper in the third bowl.
03 - Heat olive oil in a skillet over medium heat. Add ground beef, breaking it apart with a wooden spoon. Season with salt, pepper, and Worcestershire sauce. Cook for 5 to 7 minutes until browned and cooked through. Remove from heat and allow to cool slightly.
04 - Add diced pickles, tomatoes, shredded cheddar cheese, ketchup, and mustard to the cooled beef mixture. Stir until all ingredients are evenly incorporated. The filling should hold together when pressed.
05 - Select the largest intact onion rings. Pack each ring with the cheeseburger filling, pressing gently to create a compact, stable filling that extends evenly through the ring opening.
06 - Dredge each stuffed ring in flour, shaking off excess. Dip into beaten eggs, allowing excess to drip off. Press firmly into the seasoned panko mixture, coating completely and evenly on all sides.
07 - Pour vegetable oil into a deep fryer or heavy pot to a depth of 3 inches. Heat to 350°F. Fry the stuffed rings in batches of 3 to 4 for 2 to 3 minutes per batch, turning once, until golden brown and crispy. Transfer to paper towels to drain.
08 - Arrange the onion ring rolls on a serving platter. Serve hot while crispy, accompanied by your choice of burger sauce, ranch dressing, or spicy mayo for dipping.