Spoon pork mixture evenly on 1 side of each tortilla; sprinkle with cheese. Fold tortillas in half, pressing gently to seal. Spread butter on both sides of quesadillas.
Heat a large nonstick or cast-iron skillet over medium heat, and cook quesadillas 2 to 3 minutes on each side or until browned. Cut each quesadilla in half for main-dish servings or in quarters for appetizer servings. Serve with desired toppings. Garnish, if desired.
Note: You can buy pork already barbecued if you want to make this easier.