How to Make It
To prepare duck, combine first 5 ingredients. Remove and discard giblets and neck from ducks. Cut off wing tips. Rinse ducks with cold water; pat dry. Trim excess fat. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Rub herb mixture under loosened skin; rub over breast and drumsticks. Cover and refrigerate 8 hours or overnight.
Preheat oven to 325°.
Combine the honey, 1 tablespoon herbes de Provence, and 2 tablespoons vinegar; set aside.
Score duck skin several times with a paring knife (do not cut into meat). Place ducks in a roasting pan, breast side up. Cover pan tightly with foil. Bake at 325° for 1 1/2 hours. Carefully remove ducks from pan. Drain and discard drippings from pan. Carefully place ducks in pan, breast side down. Cover and bake at 325° for 1 1/2 hours.
Carefully remove ducks from pan, and discard the drippings. Cool the ducks slightly. Remove and discard skin. Carefully place ducks in pan, breast side up. Baste with honey mixture. Bake, uncovered, at 325° for 30 minutes, basting every 10 minutes. Let stand 10 minutes. Reserve drumsticks. Remove remaining meat from bones; discard bones.
To prepare lentils, stud the shallot halves with cloves. Combine shallot halves, water, lentils, and 2 garlic cloves in a large saucepan; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until lentils are tender. Remove from heat; let stand 10 minutes. Drain and discard shallot halves.
Bring 1 cup vinegar to a boil in a small saucepan. Cook until reduced to 1/4 cup (about 10 minutes). Stir in mustard and 1/4 teaspoon salt; set aside.
Heat oil in a large nonstick skillet over medium-high heat. Add chopped shallots, carrot, 2 teaspoons thyme, and 1/4 teaspoon pepper; sauté 3 minutes. Add shallot mixture and mustard mixture to lentils; toss well. Place lentils on a platter. Arrange drumsticks around lentils; top lentils with pulled meat. Garnish with thyme sprig, if desired.