In medium mixing bowl, whisk together the vegetable oil, sugar, thyme, salt, allspice, paprika, garlic powder, onion powder, cayenne, ginger, cloves, cinnamon and black pepper until a paste forms.
Blot all chicken pieces dry and pierce several times with a fork to penetrate the skin. Place into a large mixing bowl and rub well with half of the spice paste. Set aside the other half. It works best to do this with clean hands.
Place in the refrigerator, uncovered, for 30 minutes.
Preheat the oven to 400°F and arrange racks so that you can fit a baking sheet on each in the lower third and middle of the oven. Line two large baking sheets with aluminum foil or parchment paper. Set aside.
Arrange chicken pieces on prepared baking sheets, making sure there is ample room around all pieces. Bake for 40-45 minutes or until chicken registers at 165°F using an instant read thermometer. Remove and allow to rest for 10 minutes.
Whisk the remaining half of the spice paste with vinegar, honey and water. Cover and set aside.
Whisk the jerk sauce again, if separated. Serve chicken drizzled with additional sauce, if desired, and fresh parsley for garnish.