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.)
Halfway through the estimated cooking time, 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, basting occasionally with the drippings in the roaster.
Check for doneness at the end of the estimated coking time 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 for 15 minutes before slicing. This allows the juices inside the ham to set.
If you don't want or need a whole ham, you can bake half a ham, but choose the butt (meatier) end rather than the shank end. Country Dijon is a milder, creamier version of Dijon mustard. If it is not available, mix 1/2 cup regular Dijon with 1/2 cup mayonnaise.
Adapted from "Georgia Cooking in an Oklahoma Kitchen" by Trisha Yearwood © Clarkson Potter 2008. Provided courtesy of Trisha Yearwood. All rights reserved.