Mix all ingredients of the dry rub (paprika through coarse salt) in a small bowl. In another small bowl combine soft butter with 4 tablespoons of the dry rub and the liquid smoke.
Gently make an opening between the skin and the meat of each chicken leg quarter and rub 1/6th of the butter mixture under the skin, spreading as much as possible.
Rub the remaining dry rub on the outside of each chicken leg quarter. Place in a large roasting pan and pour in the water. Cover with aluminum foil and place in the oven. Roast 30 minutes. After 30 minutes, remove the foil, baste the chicken with the drippings in the pan and roast uncovered for another 30 minutes or until chicken is done.
Bring chicken broth to a boil in a large sauce pan. Gradually drizzle in the cornmeal, stirring constantly with a wire whisk to avoid lumps Reduce heat to medium low, cover and cook for 5 minutes stirring occasionally to avoid sticking. Stir in cheddar cheese, garlic powder and hot sauce. Mix well and season with salt and pepper to taste.
To serve pour the polenta on a large serving platter and arrange the chicken around it. Garnish with chopped scallions.