Remove the beef shanks from their wrappings, pat gently with paper towel to remove any excess moisture, and let come to room temperature for a half hour on a plate.
In a large, heavy-bottomed pot, preferably a dutch oven, place two tablespoons of beef tallow or olive oil, and bring to medium-high heat.
Season the beef shanks with your salt and pepper on both sides, tie gently around the outside to ensure the pieces don’t entirely fall apart, and dredge in the four.
Lay in your shanks in the pot after the pan begins sizzling and smoking, brown well on both sides, and remove from the pot onto a clean plate.
Turn the heat down to medium, and place the carrots, onion, and celery in the pot and season with more salt, while sauteing for about 10 minutes until vegetables are soft.
Add the tomato paste, and incorporate well for a few more minutes while the raw tomato flavor cooks out.
Add the beef shanks back to the pot with the wine and vinegar, and cook while stirring gently for a few more minutes to cook off the alcohol.
Next, raise the temperature to high while adding two cups of your beef broth and the bouquet garni.
Bring to a high simmer, and reduce the heat to low, and gently cook for 90-120 minutes as the meat begins to tenderize and fall off the bone. Be sure to check on the meat every 15-30 minutes, and occasionally rotate the shanks to ensure they braise evenly, and add a half cup of stock at a time as needed to ensure the shanks are always at least ⅔ of the covered with liquid.
When finished cooking, remove the bouquet garni, and compost the herbs. Then, carefully remove the shanks from the pot, and cut off their twine.
Plate up the osso buco with a bit of the drippings poured on top, serve with warm polenta, and garnish with a spoonful of gremolata. Enjoy!