Make the crust: In the bowl of a stand mixer fitted with the paddle attachment, add the flour, sugar, and salt. Add the cold butter, and mix on medium-low speed until the butter has broken down into pea-size crumbles. Turn down the mixer to low speed and drizzle in ¾ cup very cold water; continue mixing until the dough just comes together.
Turn out the dough and separate out one-third from the rest; press the 2 resulting uneven pieces of dough into 1-inch-thick disks. Wrap each tightly in plastic wrap and refrigerate for at least 1 hour or overnight.
In a large bowl, combine the rabbit, pork belly, stew meat, lamb, hen legs, duck legs, onions, and garlic. Add half each of the savory, cinnamon, and clove, and season with salt to taste. (For homemade stock, use about 1 tablespoon kosher salt and 1 teaspoon black pepper; use less for store-bought stock depending on its salt level.) Add the wine and mix well to coat the meat evenly with the marinade. Cover and refrigerate at least 8 hours, or overnight.
About 8 hours before you plan to serve the cipaille, assemble the pie. Retrieve the dough and let soften at room temperature for 10–15 minutes. Meanwhile, preheat the oven to 400°F and set a rack near the bottom with no other racks above it. Place a rimmed baking sheet or a large roasting pan on the floor of the oven to catch any drips.
Grease the bottom and sides of a deep, 3½-quart ovenproof casserole with butter. In a medium bowl, add the potatoes, remaining spices, and some kosher salt and pepper; toss and set aside. Retrieve the marinated meat from the fridge and set the duck drumsticks and hen legs aside. In a small bowl, whisk the yolks and heavy cream, and set aside.
On a lightly floured work surface, using a lightly floured rolling pin, roll out the larger disk of dough to a 16-inch circle about ⅛ inch thick. Gently lift and settle the sheet into the casserole, pressing it to fill the corners and line the sides of the dish with about 1 inch overhang around the top edges of the pot. Place the marrow bone upright in the center of the casserole. Next, cover the bottom of the casserole with a layer of mixed meats and onions. Add half of the potatoes, followed by another layer of meats. Add the remaining potatoes, followed by any remaining meats; arrange the reserved hen legs and duck drumsticks so that the bones stick up over the surface of the dish, then add enough stock to just cover the filling. (Reserve the remaining stock for basting.)
Lightly flour a work surface again, and roll out the remaining dough disk to an 11-inch circle. Use a paring knife to cut 5 small Xs in the dough where the bones will poke through. Lift and place the dough onto the top of the pie, carefully settling the openings around the bones. Pinch the seam all the way around the rim of the pot to seal, trimming away any excess dough. Brush all over with the yolk wash.
Bake for 20 minutes, then lower the temperature to 300°F and continue baking. Once the top layer of dough no longer looks raw (after about 1 hour of cooking), baste the top of the pie with the remaining stock every 30 minutes. Continue baking until the duck legs are very tender and break apart when prodded with a fork, 5–6 hours. The crust should be very dark, but if it starts to burn before the meat is tender, cover the surface with foil and finish cooking. If the drips on the tray at the bottom of the oven start smoking, swap out for a clean tray.
Let the cipaille rest at room temperature for about 1 hour before serving to allow the meats to absorb some of the juices. (The pie will be soupy inside.) Serve scooped into bowls.