Preheat your oven to 325°F (160°C).Season the pork shanks generously with salt and pepper on all sides.
Heat the vegetable oil in a large oven-safe pot or Dutch oven over medium-high heat.Place the pork shanks in the pot and sear them until golden brown on all sides, approximately 3-4 minutes per side. Remove the shanks from the pot and set them aside.
In the same pot, add the chopped onion, carrots, celery, and minced garlic. Sauté the vegetables for 5 minutes or until they begin to soften.
Add the bay leaf, thyme sprigs, chicken or vegetable broth, and red wine (if using) to the pot. Stir to combine.Return the pork shanks to the pot, nestling them among the vegetables and liquid.
Cover the pot with a lid and transfer it to the preheated oven.Allow the pork shanks to cook in the oven for 3-4 hours or until the meat is tender and easily pulls apart with a fork.
Once the pork shanks are cooked, remove them from the pot and transfer them to a serving platter.
If desired, you can strain the remaining liquid in the pot to remove the vegetables and skim off any excess fat. This liquid can be used as a flavorful sauce to drizzle over the pork shanks.
Serve the pork shanks with the sauce, if desired, and garnish with chopped fresh parsley for added freshness and color.