Begin by preparing the chicken: Preheat the oven to 450 degrees. Place the chicken on a foil lined sheet sheet. Top with two tablespoons of the butter, the oil, the garlic, and salt and pepper.
Bake for twenty minutes or until they reach an internal temperature of 165 degrees. Let sit for ten minutes and then cut in half inch pieces.
While the chicken bakes, make the Blue Cheese Dressing: Simply combine all the ingredients in a food processor.
Also, make the Fresh Tomato Salsa: Combine all the ingredients in a bowl.
Also, make the Buffalo Sauce: Melt four tablespoons of butter in a three quart saucepan on low heat. Add the rest of the ingredients and stir until combined. Stir in the cooked chicken cubes.
Lay out the four tortillas, and cover half of each one with equal amounts of the cheese and the chicken. Fold them in half. Heat a cast iron skillet with the oil on medium heat and cook each folded quesadilla until the cheese is melted. Serve with the salsa and blue cheese dressing.