In a small saucepan combine the bourbon, sugar, cola, mustard and fresh thyme. Simmer gently over low heat stirring to dissolve sugar. Reduce until thick and syrupy and liquid coats the back of a wooden spoon.
Take ham out of plastic and score (lightly cut) the top of the skin with a sharp knife. Make large cuts in one direction across the ham and then in the other direction to form a pattern of large diamonds. Place it in a large roasting dish fat side up and make sure it is brought to room temperature if refrigerated (approximately one hour). Pour and brush the glaze over the ham and add 1 cup of water with 3 tablespoons of bourbon to the bottom of the roasting pan before baking. Pop it into the oven on the lower rack.
Bake for 90 minutes, basting with pan juices every 30 minutes. Check for internal temperature -- it should reach 140 F on a meat thermometer and the meat should be tender and falling apart when done. When done, remove from oven, tent loosely with foil and let stand for 15 minutes.
Skim fat from pan juices and drizzle juice over carved ham slices.