Preheat oven to 190° C (375° F). In a small bowl, mix the four seasonings well with the lime zest and juice. Loosen the skin on the duck legs in a few places and insert a little (about a third) of this mixture under the skin with a teaspoon, then brush the legs with the liquid.
Place the duck legs on a large baking sheet and place on the middle rack of the oven. Bake the duck legs for 60 minutes.
In the meantime, put the sweet potato cubes in a large bowl and sprinkle with the remaining lime juice mixture. Moisten generously with olive oil and mix.
Remove the duck legs from the oven and arrange the sweet potatoes around them. Baste the legs with the remaining juice from the bowl, then put back in the oven. Continue cooking for another 60 minutes.
The legs are ready when the meat comes off the bone easily or when the internal temperature reaches 82° C (180° F). To brown the duck legs, broil for the last 5 minutes of cooking, if desired.
Remove from the oven and serve each duck leg on a bed of sweet potatoes, accompanied with green salad and lime wedges.
Recipe developed by Nicolas Vallée, professional chef