Preheat the oven to 400 F. Lightly grease a cookie sheet with non-stick cooking spray.
In a large skillet, brown the ground beef with the minced onion and garlic powder. Drain if needed, and then stir in the paprika, ketchup, mustard and pickles. Remove from heat.
Lay the tortilla on the baking sheet and sprinkle the shredded cheese blend onto half of the tortilla. (You will be folding the tortilla, so sprinkle a thin layer over half.) Top with the browned, seasoned ground beef. Then sprinkle more shredded cheese on top of the beef. Fold the tortilla over to cover the cheese.
Repeat with the remaining 3 tortillas, beef and shredded cheese. 4 half-tortillas should fit on a standard size cookie sheet.
Bake in the preheated oven for 8 minutes, then carefully flip and cook another 5 minutes. You want both sides to be slightly golden and the cheese melted through.
While the quesadillas are in the oven, mix up the special sauce in a small bowl. Stir together the ketchup, mayonnaise, chopped pickles and vinegar. Keep in the fridge until ready to serve as dipping sauce.
Run a knife of pizza wheel through the quesadilla and cut into wedges.
Serve Burger Quesadillas with side of fruit and/or salad.