Preheat oven to 350°F (180°C). Set ham on a rack in a foil-lined roasting pan. Add 1 1/4 cups (300 mL) root beer to pan, making sure ham is not sitting in root beer. Cover with foil and bake, 1 hour.
Meanwhile, combine remaining root beer in a saucepan with honey and ginger. Simmer until syrupy, about 10 min. Set glaze aside.
Remove ham from oven and cut off and discard skin to expose layer of fat underneath. Score a diamond pattern into fat, but do not cut into meat. Stud each diamond with a clove.
Mix together brown sugar, mustard, salt and pepper. Spread mixture evenly over ham. Then pour root beer glaze over the ham, using a brush to push it into the score marks. Return ham to oven and bake, uncovered, for 1 hour, basting twice with the pan juices, until a meat thermometer reads 160°F (71°C) and the ham is a shiny, golden brown. Remove from oven, cover loosely with foil and let rest, 15 min. Baste again with pan juices before slicing and serving.