Preheat oven to 250 degrees F.
Mix flour, salt and pepper together.
Coat dry, room temperature pork shanks with the seasoned flour.
Heat oil in dutch oven. When hot, sear the pork chops until brown on all sides. Set seared pork chops aside.
Add butter to the dutch oven. When melted, cook onions and celery until soft and beginning to brown. About 6 minutes.
Add thyme sprigs in the dutch oven and place pork chops on top of the thyme and vegetables.
Pour beef over the shanks. Add the broth until the shanks are almost completely submerged.
Bring the mixture to a simmer, cover the dutch oven and place in the preheated oven.
Cook until meat is tender and falling off the bone. Approximately 4-5 hours.
Serve with your favorite starchy side dish and drizzle the remaining sauce over the meat.
Optional for a thicker gravy: Strain braising liquid into a separate saucepan and simmer until reduced by about a third. Season with salt and pepper to taste.
*Ours is pictured with a manchego polenta.