Prepare the Onions: Melt butter in a skillet over medium heat. Add sliced onions and cook until softened and caramelized, about 10-15 minutes, stirring occasionally. Season with salt and pepper. Set aside.

Form the Patties: Divide the ground beef into 8 equal portions (about 2 ounces each). Gently form each portion into a loose ball.

Smash the Burgers: Heat a large cast-iron skillet or griddle over medium-high heat until very hot. Place two beef balls onto the hot surface. Immediately smash them very thinly using a sturdy spatula or burger press. Season generously with salt and pepper.

Cook the Burgers: Cook for 2-3 minutes per side, or until the edges are crispy and the center is cooked to your desired doneness.

Assemble the Quesadillas: Place a tortilla on a clean surface. Layer with two slices of cheddar cheese, two smashburger patties, some caramelized onions, and two more slices of cheese. Top with another tortilla.

Cook the Quesadillas: Return the skillet to medium heat. Place the quesadilla in the skillet and cook for 2-3 minutes per side, or until the tortilla is golden brown and the cheese is melted and gooey. You can use a spatula to gently press down on the quesadilla to ensure even cooking and melting.

Serve: Remove the quesadilla from the skillet and let it cool slightly. Cut into wedges and serve immediately with your favorite toppings.

Repeat: Repeat steps 5-7 for the remaining quesadillas.