Heat oven to 325. Have ready a shallow roasting pan fitted with a sturdy metal rack.
Cut rind off ham to expose fat. Place ham on rack and cover loosely with foil. Bake 1 hour and 15 minutes. Stir glaze ingredients until coffee dissolves. Brush on ham.
Bake uncovered 40-60 minutes longer, brushing twice with glaze, until meat thermometer inserted in thickest part registers 140 degrees. Let ham rest 15 minutes before slicing.