Preheat the oven to 300 degrees F.
Rinse the duck inside and out and pat dry. Trim any excess fat from the neck and cavity, snip off wingtips and discard. Mix 1 tablespoon salt and 1/2 teaspoon pepper in a small bowl, and sprinkle the bird inside and out. Using a paring knife, make dozens of slits through the skin and fat (taking care not to pierce the meat) all over both sides and all parts of the bird.
Put the duck breast-side up on a rack in a roasting pan and roast for 1 hour. Take the bird out of the oven, transfer to a platter and carefully drain the fat from the pan into a measuring cup (you'll end up getting 2 to 3 cups). Return the duck to the pan, prick with the knife again, turn it breast-side down and roast another hour. Repeat each hour, roasting the duck for a total of 4 1/2 hours.
While the duck cooks, make the sauce: In a small saucepan, heat 1 tablespoon duck fat over medium heat and cook the shallots until soft, about 4 minutes. Add the garlic and cook until fragrant, 1 minute. Add the cherries, stock, preserves, honey and rosemary, and simmer until slightly thickened, about 10 minutes. Remove from the heat, add the lemon juice, swirl in the butter and taste for salt and pepper. Set aside until the duck is finished.
After 4 1/2 hours of roasting, turn the oven temperature up to 350 degrees F, prick the duck skin one last time, salt the skin again and return bird to the oven, breast-side up. Roast for 30 minutes until the skin is nicely browned.
Remove from the oven, tent with foil and let rest for 20 minutes. Gently reheat the sauce over low heat. Carve the duck, put the pieces on a serving platter and serve with sauce.