Preheat oven to 300°F. Sprinkle pork with 1 tablespoon of salt and 1 teaspoon of pepper. Place the pork in a large roasting pan, fat side up.
In a medium saucepan, over medium-low heat, melt the butter. Add garlic, onion, fennel seeds, ½-teaspoon salt, and ¼-teaspoon ground pepper. Stir, until onion is translucent. Add sugar, vinegar, and water. Cook until the sugar dissolves completely.
Add the sugar-vinegar mixture to the bottom of the roasting pan. Cover the roasting pan with aluminum foil and place in the oven. Roast for 5 hours, basting with the sugar-vinegar mixture every 30 minutes. After 5 hours, remove the aluminum foil and increase the oven temperature to 350°F, roast for one more hour. Remove the roasting pan from the oven; baste with sugar-vinegar mixture. Allow the meat to rest for 25 minutes before carving.
Serve with roasted carrots, onions, and fennel. Garnish with fresh tarragon.