Preheat the oven to 375°F and position the oven rack in the middle. In a large skillet over medium heat, melt butter. Add onions and celery, cooking until soft (3 to 4 minutes). Add garlic and sausage, cooking until the sausage is browned (about 5 minutes). Add wine, rosemary, and thyme, cooking for an additional 2 minutes. Remove from heat.
In a large mixing bowl, combine egg, stuffing cubes, chicken broth, parsley, ½ teaspoon kosher salt, ¼ teaspoon pepper, and the sausage mixture. Stir until the bread is evenly moistened. Place the butterflied turkey breast skin-side down on a countertop. Cover with plastic wrap and, using a meat mallet or rolling pin, pound to an even ½-inch thickness. Rub the meat with 1 tablespoon of oil, and sprinkle with 1 teaspoon kosher salt and ½ teaspoon pepper.
Spoon about half of the stuffing in an even ½-inch layer over the breast, leaving a 1-inch border. (Extra stuffing can be baked separately in a buttered 8-inch dish during the last 40 minutes of the turkey's cooking time.) Roll the turkey into a long cylinder, starting at the end with less skin. Tie with kitchen string, leaving about 2 inches between each knot. Trim the strings.
Line a baking sheet with aluminum foil, place an oven-proof rack on top, and spray the rack with nonstick cooking spray. Put the turkey seam-side down on the rack, drizzle with the remaining tablespoon of oil, and season with 1 teaspoon kosher salt and ½ teaspoon pepper.
Roast for about 1 hour and 15 minutes or until the internal temperature reaches 155°F. Remove from the oven, let it rest loosely tented with foil for 15 minutes (the temperature will rise to 165°F). Snip and discard the kitchen twine, transfer the roll to a cutting board, and slice into ½-inch thick slices. Arrange on a platter and serve with homemade gravy.