Season both sides of the elk shank with salt and pepper.
Dredge the shanks in flour. Covering all sides.
Heat oil in a large 6-quart stainless steel pot or dutch oven. Lightly shake off excess flour and brown all sides of the shanks on medium heat. 2-3 minutes each side.
Remove the elk shanks from the pot and set aside.
Add 1 tbsp of butter to the pot and saute the onion until fragrant and begins to soften.
Add the chopped carrots, celery, and garlic and saute for 8-10 minutes.
Once the vegetables begin to soften, add the dry red wine to deglaze the pan, about 3-4 minutes.
Add the broth and place the elk shanks back into the pan.
Add chopped tomatoes, tomato paste, bay leaves, and thyme.
Decrease the heat to low and simmer for 2.5 hours, stirring occasionally. Keep an eye on the liquid level. Add more broth if needed.
Add salt and pepper to taste.
Add mushrooms and parsley and continue to cook for 1 more hour or until the meat is falling off the bone.
Remove the bay leaves from the pot.
Place the shanks on a platter, top with the sauce, and garnish with the remaining chopped parsley.
Serve with garlic mashed potatoes, risotto, or polenta.
Enjoy!