In a medium skillet, saute the bacon until crisp. Add the mushrooms, season with salt and pepper and cook, stirring occasionally, until the mushrooms are soft and lightly caramelized and have released their liquid, 3 to 4 minutes. Add 1/4 cup of the shallots, the celery, 1 1/2 teaspoons of the garlic and the thyme and cook until the shallots are soft, 1 to 2 minutes. Transfer the mushroom mixture to a bowl and add the white rice, wild rice, melted butter, 1/4 cup of the broth, 2 tablespoons of the green onions and 2 tablespoons of the parsley and stir to combine. Season, to taste, with salt and pepper. Add the egg, bread crumbs and pecans, stir to combine, and set aside to cool slightly before proceeding.
On a large cutting board, place the turkey breast on top of a sheet of plastic wrap and cut the breast so that it opens up to 1 large flat piece of even thickness. Cover with another sheet of plastic wrap and pound to an even thickness of just under 1/2-inch. Remove the plastic wrap from the top of the turkey and spread the stuffing evenly over the turkey breast, spreading to within 1 1/2-inches of the edges. Roll the turkey breast up, jelly-roll fashion, and tie the roulade in 2-inch intervals with butchers' twine. Season the outside of the breast liberally with salt, pepper, and poultry seasoning.
Preheat the oven to 375 degrees F.
Heat a large ovenproof nonstick skillet or small roasting pan over high heat. When hot, add the vegetable oil and when the oil is very hot but not smoking, add the roulade and cook, turning occasionally, until golden brown on all sides, 4 to 6 minutes. Add 1/2 cup of the wine and 3/4 cup of the remaining chicken broth to the pan and transfer to the oven. Roast, uncovered and turning occasionally, until the turkey is cooked through and a thermometer inserted into the center of the meat registers 155 degrees F, about 1 hour and 15 minutes, adding a bit more broth or water, as necessary, to keep juices from evaporating on the bottom of the pan. Transfer the roulade to a cutting board and let rest, covered loosely with foil, for at least 15 minutes before carving.
While the roulade is resting, place the skillet on the stovetop and add the remaining shallots, garlic, and wine to the pan and cook over high heat until the shallots are soft and the wine is almost completely reduced, scraping to release any browned bits from the bottom of the pan. Add the remaining chicken broth and cook until reduced enough to coat the back of a spoon. Add the heavy cream, remaining parsley, remaining green onions and cook until reduced slightly, 2 to 3 minutes. Season with salt and pepper, to taste, add the butter and whisk to combine. Keep warm until ready to serve the turkey. Do not allow the sauce to boil.
When ready to serve the turkey, remove the butchers' twine, slice the roulade crosswise into 1-inch slices, and serve with the sauce.