Combine the water, sugar, and kosher salt in the bowl of a stand mixer fitted with the dough hook attachment, and sprinkle the yeast on top. Allow to sit for 5 minutes or until the mixture begins to foam. Add the flour and mix on low speed until well combined. Increase the speed to medium and knead until the dough is smooth and pulls away from the side of the bowl, approximately 4 to 5 minutes. Cook's Note: Kneading the dough can also be done by hand.
Remove the dough from the bowl, clean the bowl and then oil it well with vegetable oil. Return the dough to the bowl, cover with plastic wrap and sit in a warm place for approximately 1 hour or until the dough has doubled in size. Knock the air out for 30 seconds by punching it down. You can now shape the dough into a ball, then place it onto a flour-dusted baking tray lined with parchment paper. Brush the top of the cornbread with egg wash, sprinkle the top with flour and coarse salt. Let it sit in a warm spot for 1 hour.
Preheat the oven at 400 degrees F.
Bake the cornbread for approximately 30 minutes or until the crust is golden brown.
Cook's Note: You can tell if it's cooked by tapping its bottom. If it sounds hollow it's done, if it doesn't then pop it back in for a little longer. Once cooked, place the bread on a rack and allow it to cool for about 1 1/2 hours.
For the stuffing:
Cube up the cooled cornbread and set aside.
In a large skillet, heat the oil over medium-high heat. Add the Morteau sausage and cook for about 5 minutes, until golden brown. Add the onions, celery, pepper, and garlic and continue cooking until translucent, about 5 minutes. Deglaze with the veal stock. Add in the cornbread. Transfer to a large bowl. Add the oysters and their liquid, parsley, paprika, and melted butter. Season the stuffing with salt, and pepper, to taste. Reserve the stuffing in the refrigerator until ready to use.
To assemble the turducken:
Spread the deboned turkey, skin-side down on a flat surface, exposing as much meat as possible. Sprinkle the meat generously and evenly with a total of about 3 tablespoons of the smoked paprika, patting the seasoning in with your hands. Cook's Note: Be sure to turn the leg, thigh and wing meat to the outside so you can season it too. Season the turkey with salt and pepper.
Then stuff some of the stuffing in the leg, thigh and wing cavities until full but not tightly packed. Cook's Note: If too tightly packed, it may cause the leg and wing to burst open during cooking). Spread an even layer of the stuffing over the remaining exposed meat, about 1/2 to 3/4-inches thick. You should use a total of about 4 cups of stuffing.
For the duck: Remove some of the fat and keep aside. Place the duck, skin-side down, on top of the stuffing, arranging the duck evenly over the stuffing. Season the exposed duck meat generously and evenly with smoked paprika, using about 1 tablespoon, and pressing it in with your hands. Season the duck with salt and pepper. Then spread about 1 cup of the stuffing evenly over the exposed duck meat, making the layer slightly less thick, about 1/2-inch thick. Repeat with the chicken and the remaining stuffing. Place an Italian truffle in the center, optional.
Enlist someone's help to close turducken. Fold the sides of the turkey together to close the bird. Have your helper hold the turkey closed while you sew up all the openings, making the stitches about 1-inch apart. When you finish sewing up the turducken on the first side, turn it over in the pan to sew closed any openings on the other side. Then tie the legs together, just above the tip bones. Leave the turducken to cook, breast-side up, in the pan, tucking in the turkey wings.
Serving suggestion: Serve with Root Vegetable Mash.
With the assistance of your helper, carefully lift the turducken into an ungreased 15 by 11-inch baking pan that is at least 2 1/2-inches deep. Cook's Note: This pan size is ideal because the turducken fits snugly in the pan and stays in the proper shape while cooking).
Place the turducken pan in a slightly larger pan with sides at least 2 1/2-inches deep, so that the larger pan will catch the overflow of drippings during cooking. Season the exposed side of the turducken with the remaining smoked paprika, patting it in with your hands. Brush with melted butter.
Bake the turducken at 325 degrees F, about 4 hours, until done, or until a meat thermometer inserted through to the center reads 165 degrees F. When done, remove the turducken from the oven and let rest for about 15 minutes
For the gravy:
Place the turducken drippings in a pot over medium-high heat. Add the stock, fresh thyme, and beurre manie. Season the gravy with salt, and pepper, to taste. Let the gravy come to a boil. Turn down heat to medium-low and let the gravy simmer for 10 minutes.
Cook's Note: Remember there are no bones to support the birds' structure.
With strong spatulas inserted underneath the bird, carefully transfer the turducken to a serving platter and present it to your guests before carving. Be sure to make your slices crosswise so that each slice contains the stuffing and all 3 meats. Serve additional bowls of the dressings on the side and serve with the gravy and the Root Vegetable Mash, if desired.
Cook's Notes: Stuffing and assembling the turducken can be done 1 day ahead and kept in the refrigerator.
Beurre manie is 2 tablespoons butter and 2 tablespoons flour. This is used to help thicken sauces.