Add vegetable oil to a large dutch oven (6-7 quarts) (or a large skillet) over medium-high heat. Sear the pork shanks for about 2 minutes on each side.
The next step is adding the mirepoix (celery, carrots and onions) and garlic to the pot. Let the vegetables cook over medium heat until they have all been lightly cooked.
Add the seared pork shanks back into the pot of tomato sauce. Cover and place into a preheated 325-degree oven and let the pork shanks braise in the sauce for 3 hours.