Place the rosemary sprigs in a large cast-iron skillet, then place the chicken, skin-side up, over the herbs.
Prepare the filling:.Beat cream cheese with a stand mixer fitted with a paddle attachment on medium speed until smooth, about 2 minutes.
Add eggs, 1 at a time, beating until each is combined.Add brown sugar, eggnog, flour, vanilla, salt, and nutmeg, beating until just combined, about 2 minutes, stopping to scrape down sides of bowl as needed.Pour into prepared crust.
Gently tap springform pan on counter 3 to 5 times to release air bubbles.Bake at 325°F for 30 minutes.. Reduce oven temperature to 250°F (do not remove cheesecake from oven), and bake at 250°F for 45 minutes.
Turn oven off (keep door closed); let cheesecake stand in oven for 45 minutes.
Remove cheesecake from oven (center of cheesecake should be almost set and jiggle slightly); let cool on a wire rack until room temperature, about 2 hours.. Cover cheesecake, and chill until cold, about 6 hours.Place oiled cooking grate over coals; open bottom and top vents of grill.
Place 2 stacks of 3 bricks on grill grate straddling the coals.(Stack bricks so that top brick is 8 to 10 inches above grill grate.).
Spray grill basket with cooking spray.Remove chicken from marinade, and discard marinade.
(Editor: Affordable Sunscreen)