Mix ground beef, Cheddar cheese, onion, dill pickles, tomato, salt, garlic powder, and pepper in a large bowl using your hands until well combined.
Lay tortillas on a clean work surface. Divide beef mixture evenly among tortillas, pressing into an even layer so it adheres to the tortillas and leaving about a ½-inch border around edges. Roll tortillas tightly into logs, pressing gently as you roll to compact the filling. Chill for about 20 minutes, if desired, for easier slicing.
Preheat the oven to 475 degrees F (245 degrees C) with a rack positioned about 6 inches from the heating element. Line a baking sheet with aluminum foil, and generously spray with cooking spray.
Slice each log into 1-inch-thick pinwheels and place, cut-side down, on the prepared baking sheet.
Bake in the preheated oven until starting to brown, about 6 minutes. Flip and continue to bake until starting to crisp in spots, about 4 minutes. Increase oven temperature to broil and continue cooking until edges are browned and crispy in spots, 2 minutes per side.
Meanwhile, for Special Sauce, stir mayonnaise, ketchup, pickle relish, white vinegar, paprika, and garlic powder together in a bowl until well combined.
Transfer pinwheels to a platter and serve with Special Sauce.
