Prepare the Pico:In a medium bowl, combine tomato, onion, jalapeno pepper (to taste,) cilantro and Juice of 1/2 a lime. Season with salt and pepper. Stir until evenly distributed. Refrigerate for 10-15 minutes or until ready to use.
Cooking the Beef:In a large skillet, cook onions over medium heat for 3-4 minutes or until golden and soft; add garlic and cook for only 1 minute. Add ground beef, cook until no longer pink. Drain any excess grease. Stir in tomato paste, oregano, cumin, chili powder, and salt. Cook over medium-low heat for 3-4 minutes or until heated through.
Assembling Quesadillas:Heat another skillet to medium-low heat. Brush pan with butter or oil,Place large tortilla over pan. On one half on top of the tortilla, add a layer of ground beef and a layer of pico de gallo, sprinkle with cheese. With a spatula fold the half of the tortilla without the meat mixture over the half with the meat mixture and press down.Cook until the bottom has browned and the cheese has melted. Remove from the pan. Repeat with remaining tortillas.
Step 3: Cut into wedges and serve with more pico, salsa, sour-cream, or guacamole.