Step 1

Put flour into a shallow wide bowl. Season lamb shanks all over with salt and pepper; dredge through the flour until coated, shaking off any excess flour.

Step 2

Heat a large skillet over medium heat; add butter and heat until foaming. Cook lamb shanks in the hot butter until golden, about 5 minutes per side. Transfer lamb shanks to a slow cooker.

Step 3

Pour wine into the skillet and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon; transfer to the slow cooker. Add tomatoes with their juice, onion, chicken broth, celery, and thyme leaves to slow cooker.

Step 4

Cook on Low until lamb is very tender and almost falling off the bone, 6 to 8 hours. Transfer lamb shanks to a platter and cover with aluminum foil.

Step 5

Transfer the sauce in the slow cooker to a large skillet; simmer over high heat until sauce is reduced to about 2 cups, 10 to 15 minutes. Season sauce with salt and pepper.