In large bowl or ziplock bag, combine buttermilk, salt and tabasco and refrigerate for 2-24 hours
Heat oven to 400. Spray broiling pan with cooking spray. Drain chicken in colander. Combine flour, salt, paprika,allspice and pepper in a large bag or bowl. Add chicken a few pieces at a time, toss to coat.
Pour oil into large skillet to reach 1/4"; heat over medium/high heat. When oil is hot but not smoking, add a few pieces of chicken. No more than 3 at a time. Cook 10 minutes than turn and cook another 10 minutes. Repeat until all chicken is fried.
Bake on, broiler pan or bakers rack for 30 minutes turning halfway through baking time. While chicken is baking, prepare the gravy.
Remove all but 3 tablespoons oil and browned bits from skillet. With wire whisk, stir in flour and cook over medium/high heat for 2 minutes, until golden brown. Stir in broth, half & Half, Thyme, salt and pepper. Bring to boil stirring constantly; boil 1 minute remove from heat.