Place diced vegetables in slow cooker.
Dice ham, reserving bone. Place diced ham and the ham bone in the crock on top of vegetables.
Sprinkle sugar, marjoram and pepper over ham and vegetables.
Pour broth and water into crock.
Cook on high 5-6 hours or low 7-8 hours.
Remove ham bone from crock.
Add milk and half & half.
Return lid to crockpot and cook 15-20 minutes more, until hot through.