Preheat the oven to 350°F.
Pat the bison shanks dry and season both sides with kosher salt and black pepper. Then, dust with the flour.
Place a Dutch oven on the stovetop over medium-high heat and add the olive oil. Add the bison shanks and brown all sides, about 3 minutes per side. Remove the browned shanks and set aside.
Add the onions, carrots, and celery to the Dutch oven. Sauté until slightly tender, about 4–5 minutes. Add the red wine and deglaze the pan, scraping the delicious bits from the bottom of the pan.
Add the garlic, tomatoes, beef stock, thyme, oregano, basil, bay leaf, and crushed red pepper. Bring it to a simmer.
Return the shanks to the pan. If needed, add more beef stock to fully cover the shanks. Cover with a lid and place in the oven. Baste the bison shanks every 30 minutes, and turn the shanks halfway through (about 1½). Braise until the meat is tender and falling off the bone.
To serve, remove the bison shanks and place them on plates. Spoon the pan sauce from the Dutch oven over the shanks and garnish with the parsley, Parmesan cheese, and a wedge of lemon.