Remove the shoulders from the marinade and pat them dry.
Heat a roasting pan and add the olive oil. Add the venison shoulders and sauté on all sides until nicely browned. Remove and set aside.
Add the onions, carrots, garlic cloves and celery to the pan and cook until well browned. Pour off any grease and add the herbs.
Add the wine and deglaze the little carmelized brown bits at the bottom of your pan, scraping them with a wooden spoon. Add the stock and tomatoes and a little salt and pepper. Return the venison shoulders to the liquid.
Tightly cover the roasting pan with tin foil and place in a 300° F – 325° F oven to braise for approximately 2 ½ hours.
When the shoulders are tender, remove the roasting pan from the oven. Remove the lid and let the shoulders rest for 10 minutes.
Carefully degrease the cooking liquid by skimming the fat off the top with a ladle.
Remove the shoulders from the pot and set aside in a warm place covered. Strain the braising liquid through a fine mesh seive. You can reduce some of this liquid in a separate sauce pan until it is thick, and pour it over your venison to serve.