1/2 cup apricot preserves (preferably without corn syrup)
3 Tbs. balsamic vinegar
1/2 tsp. crushed red pepper flakes
1/4 tsp. chopped fresh rosemary
Kosher salt
Vegetable oil for the grill
One 4-lb. chickens, each cut into 8 pieces, or 3 to 4 lb. good-quality bone-in skin-on chicken thighs, drumsticks, and breasts, each breast half cut into two pieces
Freshly ground black pepper
In a small saucepan, melt the butter over medium heat. Add the preserves, vinegar, red pepper flakes, rosemary, and a large pinch of salt; stir to combine. Bring to a boil, reduce the heat to medium low and simmer, stirring occasionally, until slightly thickened, 3 to 5 minutes. Remove from the heat and let cool to room temperature. (If making ahead, store covered in the refrigerator. Before using, warm over low heat to loosen the consistency.)
Turn your oven to Broil. Season the chicken lightly with salt and pepper. Set the parts skin side up on the baking pan/cookie sheet, about 5-6 inches from the heat. Cook until the skin is golden brown, about 10 minutes. Flip the chicken (with tongs - not a fork) and cook until an instant-read thermometer reads 165°F in the thickest part of each piece, 7 to 10 minutes more. The thighs, legs, and thinner breast pieces are apt to cook a little faster than the thicker breast pieces. Transfer each piece to a platter when done and tent with foil.
When all the chicken is done, brush it with the glaze on all sides. Return the chicken to the grill and cook for another minute or so on each side to caramelize the glaze. Brush the chicken with any remaining glaze and serve.