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Combine cola and salt in a medium-size cooler or other 10-quart bucket or stockpot; stir to dissolve the salt.
Using a sharp knife, score entire surface of ham in a crosshatch or diamond pattern, cutting down just through the skin. Place ham in the brine, submerging completely. Cover and refrigerate for 12 to 24 hours.
Position oven rack in the lowest position and preheat oven to 500° F.
Combine parsley, oil, garlic and bouillon in small bowl; stir well.
Remove ham from brine. Rinse it well under cold water then pat dry with paper towels. Place the ham wide-side-down in a large roasting pan with a flat rack. Rub outside of ham all over with the bouillon mixture, pressing it gently into scored slices between the skin.
Bake uncovered for 20 minutes. Reduce oven temperature to 350° F and continue to bake until the roast reaches 150° F on an instant-read thermometer (this should take 2 to 2 1/2 hours, about 20 to 25 minutes per pound of ham). After the first hour, it’s a good idea to loosely wrap foil around the bone to keep it from burning.
Transfer the roast to a carving board and tent with foil; allow the roast to sit at room temperature until the internal roast temperature reaches 160° F (about 20 to 30 minutes). The roast is now ready to carve.