Season pork shanks with salt and pepper. Tie each with kitchen twine.
Heat oil in a Dutch oven over medium-high heat. Brown pork shanks on all sides. Remove and set aside.
In the same pot, sauté onion, carrots, and celery until softened, about 5 minutes.
Add garlic and cook for 1 minute.
Pour in wine and simmer for 3 minutes.
Add tomatoes, broth, bay leaves, and thyme.
Return pork to the pot. Bring to a simmer, cover, and cook on low for 2 hours or until meat is very tender.
Remove twine before serving.