In a medium bowl, mix together mayo, grated onion, ketchup, pickle relish, yellow mustard, white vinegar, and paprika. Whisk until smooth and creamy. Refrigerate while you prepare the quesadillas.

Heat a large skillet over medium-high heat. Add ground beef, breaking apart as it cooks. Brown for 5-7 minutes until fully cooked. Drain excess grease, season with salt, black pepper, garlic powder, and Worcestershire sauce. Stir to combine and remove from heat.

Take a flour tortilla and lay it flat. On one half, layer cheddar cheese, a portion of the ground beef, chopped onions, and sliced pickles. Top with another layer of cheese and fold the tortilla in half.

In the same skillet, heat olive oil over medium-high heat. Place the quesadilla in the skillet and cook for 2-3 minutes on each side until golden brown and crispy, and cheese is melted.

Remove from skillet, allow to cool briefly, and cut into triangles. Serve with the burger sauce for dipping.