In a bowl, crush the garlic and the thyme with the back of a spoon. Season the quail with a little salt and pepper, then rub with the garlic and thyme. Allow marinating for 1 hour in the refrigerator.
Preheat oven at 375 degrees F.
Brush both sides of the quail with the B.B.Q. sauce. Put quails on a rack in a baking dish. Bake for 15 minutes.
Remove quail from the oven and turn on the broiler. Brush quails with more sauce. Place quails under broiler to char, about 6 minutes. Turn to char both sides.