In a large bowl, combine flour, salt, egg whites, 2 tbsp. pepper, rosemary, thyme, and cilantro and mix until dough holds together. Turn dough out onto a lightly floured surface and knead until smooth and elastic, about 2 minutes. Form dough into a ball, wrap in plastic, and refrigerate for 30 minutes.
Preheat oven to 450°. Rinse duck, pat dry, then prick skin with a fork. Season inside and out with salt and pepper. Heat oil in a large skillet over medium-high heat, then sear duck, turning to brown on all sides, 10–15 minutes. Transfer duck to a plate and set aside to cool.
Turn dough out onto a lightly floured surface. Roll out into a 10'' x 14'' rectangle. Place duck in center of dough, breast side down, then wrap dough around duck, pinching to seal. Place duck, seam side down, on a baking sheet and bake for 30 minutes. Remove from oven.
Meanwhile, place vinegar, wine, shallots, and bouquet garni in a saucepan. Simmer over medium-high heat until reduced by three-quarters, about 7 minutes. Add honey, chicken stock, and veal stock. Cook until sauce is slightly thickened, about 5 minutes more, then strain, season with salt and pepper, and keep warm.
To serve, use a sharp knife to cut through crust, then peel away and discard. Thinly slice breast meat and arrange on 4 plates. Spoon sauce over meat. Cut legs (with thighs) from duck and return them to oven, cooking until skin is crisp, 15–30 minutes. Serve legs as a second course.