In a bowl, mix jerk seasoning, olive oil, soy sauce, brown sugar, and minced garlic.
Coat chicken thighs with the marinade, ensuring they are well-covered.
Refrigerate for at least 2 hours or overnight for maximum flavor.
Melt butter in a saucepan over medium heat.
Add heavy cream, stirring until it simmers.
Gradually whisk in Parmesan cheese until smooth.
Season with salt and pepper to taste.
Grill marinated jerk chicken until fully cooked, then slice into strips.
Spread Alfredo sauce generously over a flour tortilla.
Place a portion of grilled jerk chicken on one half of the tortilla.
Sprinkle mozzarella cheese over the chicken and fold the tortilla in half.
Heat a skillet over medium heat and lightly coat with cooking spray.
Cook the quesadilla for 2-3 minutes on each side until golden brown and crispy.
Repeat for the remaining quesadillas.