In a large stockpot, combine the apples with the apple juice. Cook on low heat until the apples are tender, about 45 minutes. Remove from heat and pass through a fine sieve. Pour the puree back in the stockpot. Bring to a simmer and add the brown sugar, cinnamon, nutmeg, and lemon juice. Cook on low heat for about 1 1/2 hours until it's reduced by half and thickens up, stirring regularly and skimming the surface if necessary. Remove from heat and let cool.
For the ham:
Put the ham, carrot, celery, leek, onion, and garlic in a large stockpot and cover with water. Bring to a boil and let simmer for 2 hours. Drain and place into a roasting pan.
Preheat the oven at 350 degrees F.
In a bowl, combine the apple butter, honey, and Dijon mustard. Peel off the skin of the ham and brush it with apple butter mixture. Pour the water in the bottom of the pan. Place in the oven and cook for 1 1/2 hours, making sure to baste it with the sauce every 15 minutes during cooking process. Remove the ham from the grill and let sit for 10 minutes before carving.
The apple butter is great on its own, with ice cream, yogurt or for breakfast.