Adjust the oven racks to accommodate a large roasting pan and preheat the oven to 350 degrees F. Fit the pan with a shallow rack.
Unwrap the ham and rinse it in cold water. Place it on the rack in the roasting pan. Cover the pan with aluminum foil, leaving a 2-inch opening to allow steam to escape. Bake the ham for half the estimated cooking time, about 3 hours. (Total cooking time is about 20 minutes per pound.)
Add the brown sugar and honey to a saucepan and cook over medium heat until the mixture is smooth and the sugar is dissolved. Remove from the heat and stir in the mustard.
Pour the mixture over the ham. Continue baking the ham, uncovered, basting occasionally with the drippings in the roaster, for the remaining time, about 3 more hours. Check for doneness by inserting a meat thermometer into a meaty part of the ham, avoiding any fat or bone. The thermometer should register 160 degrees F.
Allow the ham to stand 15 minutes before slicing. This allows the juices inside the ham to set.