1: Set up your grill for direct grilling and heat to high. Brush and oil the grill grate.
2: Using a sharp knife, score the skin side of the duck legs in a crosshatch pattern. (Do not nick the meat.) This helps release the fat. Generously season the duck legs on all sides with salt and pepper.
3: Heat the olive oil in the skillet on the hot grill. Add the duck legs, skin side down, and cook until the skin is crisped and browned, about 2 minutes. Turn the duck legs over and brown the meaty side the same way. Transfer the duck legs to a platter. Pour the extra duck fat into a heatproof jar and save for future use.
4: Add the Armagnac and boil until only 2 tablespoons remain. Add the red wine and boil until only 1/4 cup of liquid remains.
5: Set your grill up for indirect grilling and lower the heat to 300 degrees. Add wood chunks or chips (the latter should be soaked in water for 20 minutes, then drained) to the fire. Return the duck legs to the pan, skin side up, and add enough stock to come halfway up the meat.
6: Indirect grill the duck legs for 1 hour, adding stock as necessary to keep the meat partially submerged.
7: Add the carrots and potatoes and continue cooking the duck until the vegetables are tender, another 45 minutes. At this point, you’ll probably need to add more stock.
8: Stir in the tomato and olives and continue cooking the duck until the meat is very tender. Again, add stock as needed to keep the meat partially submerged.
9: Taste the sauce, adding salt and pepper to taste. But remember: the olives are salty already. Serve at once with a gutsy bottle of red wine, like a Cahors or Chiroubles.
