Place ham fat side-up on a rack in a roasting pan. Score ham fat in a crisscross design; season with sea salt.
Mix brown sugar, sorghum syrup, brown mustard, brandy, dry mustard, cinnamon, nutmeg, and ginger together in a bowl for the basting mixture. Brush 1/3 basting mixture on top of ham and stick cloves into fat. Pour coffee into bottom of roasting pan.
Cook ham in the preheated oven, brushing with remaining basting mixture every 30 minutes, until an instant-read thermometer inserted in the center reads 165 degrees F (74 degrees C), about 2 hours total.