To butterfly chicken, start by removing neck, giblets, and cut away excess fat. Next, take a pair of kitchen shears and cut along both sides of backbone to remove. Turn chicken over skin side up and press down between the breasts to break the keel bone (this will allow the chicken to lay very flat on grill).
In a small bowl, combine jerk seasoning, cloves, and cinnamon. Sprinkle liberally over all sides of chicken; set aside. Chicken can be prepared up to this point a day ahead.
For glaze: In a small pot over medium-high heat, combine all glaze ingredients. Bring to boil and cook until glaze thickens, about 15 to 20 minutes. Remove from heat; set aside.
Set up grill for indirect grilling over medium heat or heat a 10-inch cast iron grill pan over medium-high heat. Oil grate when ready to start cooking.
Place the chicken in the skillet skin side down and cook until skin is crisp and has nice grill marks. Brush the flesh side with the glaze, then turn the chicken over and brush the skin side. Transfer the grill pan to the oven and bake until chicken is cooked golden and the internal temperature of the thigh registers 180 degrees F on an instant-read thermometer, about 30 minutes. Transfer to cutting board; let rest 5 minutes before cutting. Serve hot.