Step 1: Divide the ground beef into 8 equal, loose balls. Season generously with salt and pepper. If using diced onion, gently mix it into the beef before forming balls.
Step 2: Heat a large cast-iron skillet or heavy-bottomed pan over medium-high heat until very hot. Add 1 tablespoon of butter or oil and let it melt.
Step 3: Place two beef balls into the hot skillet. Immediately use a sturdy spatula to firmly smash each beef ball into a thin patty (about 1/4 inch thick). Cook for 2-3 minutes until a deep brown crust forms.
Step 4: Flip the patties. Immediately place one slice of cheese on each patty. Cook for another 1-2 minutes until the cheese is melted and bubbling.
Step 5: Place one large tortilla over the two cheeseburger patties in the skillet. Gently press down so the tortilla adheres to the cheese. Cook for about 1 minute.
Step 6: Carefully slide the spatula under the tortilla and flip the entire assembly (tortilla with patties attached) over. Cook the tortilla side for 1-2 minutes until golden brown and crispy.
Step 7: Add desired toppings (like shredded lettuce, pickles, or a drizzle of burger sauce) onto one half of the tortilla, over the cheeseburger patties. Fold the other half of the tortilla over to create a quesadilla.
Step 8: Remove from skillet, slice in half, and serve immediately. Repeat with remaining beef balls, cheese, and tortillas, adding more butter/oil as needed for subsequent batches.