Bring a large skillet or griddle to medium heat. Assemble a quesadilla on a cutting board. Divide the three cups of shredded pepper jack cheese into four even portions.
Sprinkle one pile of shredded cheese over half of one tortilla. Add half of the cooked chorizo, followed by half of the caramelized onions, distributing them each evenly. Top with another of the piles of shredded cheese.
Fold the naked half of the tortilla over the top of the side with fillings. Repeat step above with the second quesadilla.
Place quesadillas into a large pan or put on a griddle (you may need to cook one at a time, depending on your cooking surface).
Cook for 5-7 minutes on each side, or until crisp and toasty looking.
Remove from heat and cut into four slices. Serve with your favorite salsa.
Feel free to experiment with whatever good melting cheese you'd like! Everything from Oaxaca to plain old cheddar work great! My recommendation is to buy a block of cheese and grate it yourself for the best results.
Keyword chorizo quesadilla, quesadilla con chorizo