How to Make It
Bone the chicken legs: Set each chicken leg, meaty side down, on a work surface. Using a sharp knife, make 1 slit from the thighbone down to the end of the drumstick. Scrape the meat from the bones; remove the bones, keeping the skin and meat intact. Using a pair of sturdy tweezers, pull out the white tendons from the drumstick.
Spread each boned leg between 2 sheets of plastic wrap and pound to a 1/2-inch thickness. Cut five 9-inch squares of foil. Lightly brush the foil with the melted butter. Discard the plastic wrap and set each chicken leg in the center of a foil square, skin side down. Sprinkle with salt and white pepper.
Pipe a 1-inch stripe of Chicken Mousse down the center of each chicken leg; fold the meat around the mousse and roll the chicken up in the foil. Twist the ends to form a tight log. Refrigerate for at least 1 hour or overnight.
Bring a large pot of salted water to a boil. Have a large bowl of ice water near the stove. Cook the beans in the boiling water until crisp-tender, about 4 minutes. Using a slotted spoon, transfer the beans to the ice water. Return the water to a boil and blanch the carrots for 6 minutes; add the carrots to the beans. Repeat with the leeks, blanching them for 2 minutes before refreshing them. Drain the vegetables.
Melt 4 tablespoons of the butter in a large saucepan. Add the shallots and garlic and cook over moderately low heat, stirring, until softened but not browned, about 8 minutes. Add the vinegar and cook over moderately high heat until evaporated. Add the wine and cook, stirring occasionally, until reduced to about 1/2 cup, about 15 minutes. Add 2 cups of the Rich Chicken Stock and boil gently until reduced to 3/4 cup, about 20 minutes. Add the cream and boil until the sauce has reduced to 2 cups, about 15 minutes. Strain the sauce through a fine sieve, pressing hard on the solids. Return the sauce to the pan and season with salt and white pepper. Whisk in the remaining 2 tablespoons of butter.
Steam the stuffed chicken legs over high heat for 25 minutes, or until an instant-read thermometer inserted in the center of a leg registers 175°. Transfer the legs to a cutting board and let stand for 10 minutes.
In a large saucepan, bring the remaining 8 cups of Rich Chicken Stock to a boil. Add the chicken breasts and simmer gently over moderately low heat until cooked, 15 to 18 minutes. Unwrap the chicken legs and cut each in half crosswise. Remove the breast meat from the bones in 1 piece and cut in half. Rewarm the blanched vegetables and the peas in the stock.
Reheat the sauce over low heat. Arrange a piece of breast and stuffed leg on each plate. Using a slotted spoon, transfer the vegetables to the plates. Reserve the stock for another use. Using an immersion blender or electric mixer, whir the sauce until frothy. Spoon some sauce over the chicken and vegetables, sprinkle with the tarragon and serve. Pass the remaining sauce separately.