Cook the cheeseburger filling. Heat a large nonstick skillet over medium-high heat. Add the ground beef and diced onion and cook, breaking the meat into small crumbles, until browned and no longer pink, about 5–7 minutes. If there is a lot of grease, carefully spoon off most of it, leaving about 1 tablespoon in the pan for flavor.Reduce the heat to medium. Stir in the ketchup, mustard, Worcestershire sauce, garlic powder, onion powder, smoked paprika, salt, and pepper. Cook for 1–2 minutes more, stirring, until the mixture is evenly coated and saucy. Taste and adjust seasoning, then turn off the heat. Assemble the quesadillas. Lay the tortillas on a clean work surface. Sprinkle about 1/4 cup shredded cheese over half of each tortilla. Spoon a thin, even layer of the warm beef mixture over the cheese (about 1/4 cup per tortilla), then top with another small handful of cheese. Sprinkle with chopped dill pickles and crumbled bacon, if using. Fold each tortilla in half to form a half-moon, or top with a second tortilla to make a full round quesadilla.
Toast until crispy and melty. Wipe out the skillet if needed and return it to medium heat. Add about 1/2 tablespoon oil or butter and swirl to coat the pan. Place 1–2 quesadillas in the skillet, without crowding. Cook for 2–3 minutes per side, pressing gently with a spatula, until the tortillas are golden brown and the cheese is melted. Repeat with the remaining quesadillas, adding more oil or butter as needed.
Slice and serve. Let the quesadillas rest for 1–2 minutes so the cheese can set slightly, then slice each into wedges. Serve hot with extra pickles, burger sauce, ketchup, or your favorite dipping sauce.