In a bowl, season the ground beef with burger seasoning. Form the beef into small balls about the size of golf balls.
Heat a non-stick skillet or griddle over medium-high heat. Add 1 tablespoon of olive oil. Place the beef balls in the skillet and smash them down with a spatula to form thin patties. Cook for 3-4 minutes on one side until browned, then flip and cook for an additional 2-3 minutes on the other side. Remove from heat.
Lay out a tortilla and sprinkle a layer of cheddar and Monterey Jack cheese across half of the tortilla. Add a layer of the cooked burger patties, onions, diced tomatoes, and pickles. Top with another layer of cheese. Carefully fold the tortilla in half over the filling.
In the same skillet, add the remaining tablespoon of olive oil. Place the folded quesadilla in the skillet and cook for about 3-4 minutes on each side, or until the tortilla is golden brown and the cheese is melted. Repeat for the other quesadillas.
Remove the quesadillas from the skillet and let them sit for a minute before slicing them into wedges. Serve with sour cream and salsa on the side.