Smash avocado in medium bowl. Add salt and pepper to taste. Spread avocado over half of each tortilla. Add diced chorizo and onion evenly over smashed avocado. Top with ½ cup shredded pepper jack cheese. (or more if you desire) Fold each tortilla.
Heat butter in large skillet over medium heat. Add both quesadillas to skillet and cook on one side for about 5 minutes or until browned. Flip both quesadillas and cook for another 5 minutes or until browned. Use the pizza cutter to cut into four slices. Serve immediately.