Lay one tortilla flat on a cutting board and spread 1/2 cup of shredded Ghost Pepper Jack cheese evenly over half of it. Fold the tortilla in half to cover the cheese.
Repeat with the remaining three tortillas and cheese until all four quesadillas are assembled.
Heat a large skillet over medium heat. Spread a thin layer of softened butter on one side of each folded quesadilla.
Place one quesadilla, buttered side down, in the skillet. Cook for 2 to 3 minutes until the bottom turns golden.
Butter the top side, flip the quesadilla, and cook for another 2 to 3 minutes until both sides are crisp and the cheese has melted.
Remove to a cutting board and let it rest for 1 minute. Cut the quesadilla into four triangles with a sharp knife.
Repeat the cooking and cutting process with the remaining quesadillas.