In a medium bowl, blend 1 1/2 sticks of the butter with the mushroom powder, shallot, parsley and lemon juice. Season with salt and pepper.
Preheat the oven to 400°. Carefully loosen the skin from the turkey breast, legs and thighs. Season the turkey inside and out with salt and pepper. Spread a thick layer of the mushroom butter under the skin; press the skin to distribute the butter evenly. Put the prunes and thyme sprigs in the cavity and tie the legs together with kitchen string.
Set the turkey in a large roasting pan. Pour 1 cup of the wine, the water and the Cognac into the pan and roast the turkey for 20 minutes. Turn the oven down to 325°, cover the turkey loosely with foil and roast for 2 hours. Remove the foil and continue to roast for about 1 hour and 15 minutes longer, turning the pan halfway through. The turkey is done when it is nicely browned all over and an instant-read thermometer inserted in the inner thigh registers 160°.
While the turkey roasts, melt the remaining 1 tablespoon of butter in a medium saucepan. Add the wing tips and neck pieces, season with salt and pepper and cook over moderate heat until browned, about 10 minutes. Add the onion and celery and cook until lightly browned. Sprinkle in 2 tablespoons of the flour and cook, stirring, for 1 minute. Slowly pour in the remaining 1/2 cup of wine and stir until smooth. Gradually stir in the turkey stock and bring to a boil. Cover and simmer over low heat until reduced to 3 1/2 cups, about 2 hours. Strain and set aside.
When the turkey is done, transfer it to a carving board and let rest for at least 30 minutes. Discard the string. Remove the prunes from the cavity; coarsely chop them. Pour the pan drippings through a coarse strainer set over a bowl. Use a ladle to skim off the fat, reserving 2 tablespoons.
In a medium saucepan, combine the reserved fat with the remaining 3 tablespoons of flour and stir over moderate heat for 1 minute. Gradually whisk in the pan drippings and the strained turkey stock. Simmer over moderately low heat for 10 minutes, whisking frequently. Remove from the heat and whisk in the foie gras mousse, 2 pieces at a time. Stir in the chopped prunes and season with salt and pepper. Carve the turkey at the table and pass the gravy separately.
Make Ahead: The wild mushroom butter can be refrigerated for 1 week. Soften before using. The finished gravy can stand off the heat for up to 1 hour. Bring to a simmer over low heat, whisking constantly; do not let it boil.