Place thawed venison shanks on rack, placed over a rimmed baking sheet, to catch drips. Refrigerate for at least 24 hours.
Remove from refrigerator 1 hour before continuing with recipe to allow meat to come up to room temperature.
Start oven at 300°F.
Melt butter and olive oil together in Dutch oven.
Brown shanks on all sides. Remove to plate.
Add onions, carrot and celery to pan, if needed add more oil or butter. Sauté vegetables, scrapping up the browned bits room the bottom of the pan.
Once golden brown, add red wine and continue to scrape bottom of pan.
Add stock, tomatoes, thyme and bay leaf. Bring to boil.
Add venison back to Dutch oven. Cover. Braise for 3 to 4 hours until shanks are very tender. Twist meat with fork. If it separates easily, the meat is done.
Remove from oven and remove shanks to a plate.
Add 2-3 tablespoons cornstarch to a small bowl. Mix in enough water to incorporate all of cornstarch. Cook over low heat until sauce is thickened, dark and glossy. Add shanks back to sauce.
Serve with mashed potatoes and your choice of vegetable.