In a small bowl, whisk together the mayonnaise, grated onion, ketchup, pickle relish, yellow mustard, white vinegar, and paprika until smooth. Cover and let chill in the fridge.

Heat a large skillet over medium-high heat. Add the ground beef and break it into fine crumbles, cooking for 5-7 minutes until fully browned.

Drain any excess grease and return the skillet to heat. Stir in salt, black pepper, garlic powder, and Worcestershire sauce, mixing thoroughly. Remove from heat.

Lay out the tortillas and place 2 slices of cheese on one half of each tortilla. Evenly distribute the seasoned beef mixture followed by onions and pickles, then top with 2 more slices of cheese. Fold the tortilla in half.

Wipe out the skillet or use a clean griddle. Heat over medium-high and add olive oil. Once hot, place the quesadillas into the pan and cook for 2-3 minutes per side until golden brown and crispy.

Transfer the quesadillas to a cutting board, let rest for a minute, then slice into triangles and serve with the chilled dipping sauce.