If desired, brine turkey breast. Rinse well, pat dry.
Preheat oven to 375° F.
On a large cutting board, place the turkey breast on top of a sheet of plastic wrap and butterfly 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 ½-inch. Remove the plastic wrap from the top of the turkey; spread the stuffing evenly over the turkey breast, spreading to within 1 ½-inches of the edges. Roll the turkey breast up, jelly-roll fashion, and tie the roulade in 2-inch intervals with kitchen twine. Season the outside of the breast with salt and pepper.
Heat a large ovenproof skillet or small roasting pan over high heat. When hot, add the olive oil. 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 ½ cup of the wine and ¾ cup of the chicken broth to the pan and transfer to the oven. Roast, uncovered, until the turkey is cooked through and a thermometer inserted into the center of the meat registers 165° F, between 30 minutes and 1 hour and 15 minutes depending on the thickness of the roulade. If necessary, add more broth or water to keep the 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 shallots and wine to the pan. 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, and green onions; cook until reduced slightly, 2 to 3 minutes. Season with salt and pepper, to taste. If necessary add beurre manié consisting of 1 tablespoon unsalted butter and 1 tablespoon flour; 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 kitchen twine, slice the roulade crosswise into 1-inch slices, and serve with the sauce. Yield: 4 to 6 servings.