With your hands, combine the ground beef with the spices (red pepper through adobo seasoning/salt). Divide the meat into four same-sized portions, then form each into a burger patty. You want thin, very flat and very round burgers.
Heat some olive oil in a skillet over medium-high heat. Fry each patty for 5-10 minutes (until desired doneness), flipping once halfway through. Alternately, you can grill or broil the burgers. Set patties aside when done and keep warm.
Wipe down the skillet and return to heat. Brush one side of each tortilla with olive oil. Place tortilla oiled-side down onto hot skillet. Place 3 tablespoons of cheese on the tortilla, leaving same space empty near the edges. Top the cheese with 2 tablespoons of pico de gallo, then top with a burger patty. Now, top the burger with 1 tablespoon chopped jalapenos and then 3 tablespoons of cheese. Finally, place another tortilla on the quesadilla with the oiled-side facing you.
Cook until the bottom of the tortilla is browned and cheese is fully melted, about 1-2 minutes. Flip, and cook another 1-2 minutes.
Repeat steps 3 and 4 until all quesadillas are constructed and cooked.
Cut each each quesadilla in half and serve right away with a bit of sour cream. Serve alongside rice & beans for a complete and satisfying meal.