Preheat oven to 350 degrees.
Place mushrooms, ½ cup parmesan cheese, artichokes, parsley, garlic, salt, and pepper in a food processor and pulse until blended.
Butterfly turkey breast, then pound turkey breast to ¼ inch thick. You should end up with about a 10x6 rectangle.
Place artichoke mixture on center of pounded turkey leaving an inch border around the edges. With long side facing you, roll away from you into medium tight cylinder. Truss turkey breast using twine. Optionally, you can wrap it with bacon strips.
Coat turkey in olive oil. Generously salt and pepper turkey. Place turkey on smoking hot skillet and brown on all sides. Remove the turkey breast from the pan.
Add onions and garlic to the pan and cook until softened, about 3 minutes. Add more olive oil if they begin to brown too quickly. Pour in the wine and cook for about a minute, then add the stock and ½ teaspoon salt. Return the turkey to the pan. Put herb sprigs on top of the turkey.
Place turkey in oven and bake for about 30 minutes or until turkey registers 140 degrees.
Transfer turkey to cutting board and allow to rest for 5- 10 minutes.
Place the pot over medium heat and scrape any bits from the bottom of the pan. Allow mixture to reduce by ¼ then add the cream and cook for another minute. Turn off the heat when gravy coats the back of a spoon.
Remove twine from the turkey and slice with ½ inch slices. Serve with the white wine gravy, along with parmesan cheese and thyme leaves.