Pat the duck legs dry with paper towels. Rub each piece generously with coarse salt, minced garlic, and black pepper. Place them on a plate, cover, and refrigerate for at least 4 hours or overnight for curing.
Preheat your oven to 225°F (107°C). Rinse the cured duck legs under cold water to remove excess salt, then pat dry thoroughly with paper towels.
Arrange the duck legs in a roasting pan or over a baking dish, placing sprigs of thyme around them. Pour melted duck fat over the legs until they are almost submerged. Cover tightly with foil.
Bake in the preheated oven for 2 ½ to 3 hours, until the meat is very tender and easily pulls away from the bone. You should see the fat gently bubbling around the edges and the meat turning a rich, dark color.
Remove the duck legs from the oven and carefully take off the foil. Heat a skillet over medium-high heat. Once hot, add the duck legs skin-side down and cook for 3-5 minutes until the skin is golden brown and crispy, listening for the satisfying crackle.
Transfer the crispy duck legs to a plate and serve immediately, or let them rest. Optionally, you can remove excess fat from the skillet, pour in a bit more duck fat to reheat, and spoon over the meat for extra flavor and moisture.
