Rinse meat under cold water and dry with paper towels. Season with salt and pepper. Add flour to a shallow dish. Dredge seasoned pork in the flour.
Heat 2 tablespoons of butter in a large skillet. When the butter foams, add the pork to the skillet. Cook until golden, searing the meat for 4 minutes on each side and transfer to your slow cooker.
Deglaze the skillet with the wine. Scrape up any browned bits from the bottom of the skillet and pour into the slow cooker. Add the tomatoes and their juices, bone broth, onion, carrot, garlic, celery, sage, oregano and a bay leaf. Cover and cook on low heat for 6 to 8 hours.
Transfer the shanks to a plate, cover and set aside. Strain the juices from the slow cooker into your skillet. Mash veggies to extract liquid as much as possible. Skim the fat off the top of the gravy.
Simmer for 10 minutes. Season with salt and pepper. Remove from the heat and stir in one stick of butter.
For the gremolata: Zest the skin of both lemons. Add lemon zest, garlic, and capers to parsley and toss in a small bowl.
Serve topped with gravy and gremolata.