1. Preheat oven to 350 degrees. Season meat with salt and pepper. Heat an 8-quart Dutch oven or other heavy-bottomed ovenproof pot over high heat. Add 2 tablespoons oil. Working in batches, brown meat on all sides, 7 to 10 minutes a batch, reducing heat if meat is browning too quickly. Transfer meat to a platter. Pour off fat and wipe pot clean.

2. Place pot over medium heat. Add remaining 3 tablespoons oil, onion, carrots, celery, and garlic. Cook, stirring occasionally, until onion is translucent, about 5 minutes. Increase heat to high; stir in tomato paste and cook 30 seconds, then add flour and cook, stirring, 30 seconds more. Add soy sauce and wine; bring to a boil. Add broth and herbs.

3. Return meat and accumulated juices to pot, bone-side up (if applicable). Bring to a boil, then cover and transfer to oven. Cook 1 hour, or 2 hours for lamb shanks. Remove lid; rearrange meat pieces on top of pot to bottom and cook until meat is very tender, about 1 hour more.

4. With tongs or a slotted spoon, transfer meat to platter. Strain liquid through a fine-mesh sieve, pressing on solids; if sauce is too thin, simmer in a saucepan until slightly thickened. Serve meat with sauce spooned over top.