1 ham bone from bone-in ham
12 cups water
1 bay leaf
1 onion, peeled
3 cloves
1 tablespoon bacon fat
2 onions, diced
1/4 teaspoon salt
1 pound potatoes, peeled and diced
1 cup half-and half
2 cups leftover baked ham, diced
Place the ham bone in a stock pot and cover with water. Add the bay leaf. Stick the cloves into the peeled onion, and add to the pot. Bring the water to a boil, then reduce to a simmer and cook, skimming the foam from the top occasionally, for 2 hours.
When the broth is cooked, remove the ham bone, bay leaf, and onion and discard. Set the broth aside.
Heat the bacon fat in a stock pot. Add the onions and the salt and cook, stirring occasionally, until soft and lightly browned, about 12-15 minutes.
Add the potatoes and 10 cups of the reserved broth. Cook, stirring occasionally, for about 30 minutes, or until the potatoes are tender.
Remove half of the soup and blend it in a blender. Return the blended soup to the pot, and add the half-and-half and leftover ham. Stir to combine. Simmer for another 5 minutes to warm through, then serve.