Wash ham, scrubbing thoroughly with a stiff brush; rinse well. Place ham in a very large container; cover with cold water. Soak overnight. Drain.
Combine vinegar, 1 cup brown sugar, and molasses in a large mixing bowl. Place ham in a large roasting pan. Pour vinegar mixture over ham, and add enough cold water to cover ham. Cover and bake at 500° until vinegar mixture boils; reduce heat to 300°, and bake 2 1/2 hours, allowing 15 minutes per pound. Turn oven off, and allow ham to cool in oven overnight. Do not open oven door.
Remove ham from pan; remove skin and discard. Place ham, fat side up, in a shallow roasting pan; sprinkle remaining brown sugar over ham. Bake at 325° for 30 minutes or until browned. Transfer to a serving platter. Cool completely. Cut into thin slices to serve.
Note: Reserve remaining ham for other uses.