Sprinkle 1 tablespoon of salt in the bottom of a dish or plastic container large enough to arrange the pieces of duck in a single layer. Spread half of the garlic, shallots, and thyme in on top of the salt in the container. Place the duck parts skin-side up over the salt mixture, and then top evenly with the remaining salt, garlic, shallots, and thyme and pepper. Cover and refrigerate for 1-2 days.
Preheat the oven to 225°F.
Melt the duck fat in a small saucepan. Remove the duck pieces from the container and lightly brush the seasonings off. Arrange the meat snugly in a single layer in a high-sided baking dish or ovenproof saucepan. Pour the melted fat over the duck (the duck pieces should be covered by fat) and place the confit in the oven.
Cook the confit slowly at a very gentle simmer until the duck is tender and can be easily pulled from the bone, 2-3 hours. Remove the confit from the oven. Cool and store the duck in the fat. Can be kept in the refrigerator for several weeks.