Preheat oven to 325°F. Place a large, heavy-bottom pot on the stove over medium-high heat. Add the canola oil and warm until hot but not smoking. Pat the beef shanks dry and season both sides liberally with salt and pepper. Working in 2 batches, add the shanks to the pot and sear for 4–5 minutes per side, until well browned. Remove to a plate and repeat with remaining shanks. Set the shanks aside.
Reduce the heat to medium-low and allow the pot to cool for 1 minute before adding the onions, carrots and celery along with ¼ teaspoon kosher salt. Turn the heat to medium and stir the veggies to coat with the fat in the pan; cook until softened and beginning to brown, 8–10 minutes. Add the garlic and red pepper flakes to the pot and toss to combine until fragrant, approximately 30 seconds, before adding the tomato paste. Stir, allowing the tomato paste to break down and to begin to melt and then add the mushrooms along with ¼ teaspoon salt and ¼ teaspoon black pepper. Cook the mushrooms for 5 minutes, stirring frequently, until they begin to soften.
Add the beef shanks back to the pot, nestling them into the vegetables as much as possible. Pour 1 bottle of Old 502 Boredough wine into the pot and stir in ½ teaspoon salt and ¼ teaspoon black pepper. Tie the rosemary, thyme and bay leaves together with a piece of kitchen twine and add to the pot. Bring to a boil, place the lid on the pot and transfer to the oven. Cook for 3 to 3½ hours, until the meat is completely tender and falling away from the bone.
When finished cooking, transfer the shanks from the pot to a plate and discard the herb bundle. Taste the sauce and add additional salt and pepper if necessary. Bring to a simmer and allow the sauce to continue to reduce over low heat, for 10 minutes. Stir 2 tablespoons of unsalted butter into the sauce and return the meat to the pot. Remove the pot from the heat, top with the lid and set aside until ready to serve.
While the braising sauce is further reducing, bring 4 cups of water to a boil in a medium pot. Whisk 1 cup of Weisenberger Mill yellow grits into the boiling water, cover and cook over low heat for 20–25 minutes, until thickened, whisking frequently. Add salt and pepper to taste. Off of the heat stir in shredded Kenny’s cheddar cheese. Divide cheese grits among 4 shallow bowls and top with the braised beef shanks. Spoon sauce over the beef and garnish with parsley before serving.