In a large Dutch oven over medium-high heat, add oil. Season lamb with salt and pepper. Add to hot oil and cook, browning each side, about 4 minutes per side (if necessary, cook in batches). Remove shanks to a clean plate and set aside.
Add onion, carrots, celery, tomato paste, herbs de Provence, garlic, salt and pepper; cook until softened, about 5 minutes. Add wine, scraping up any brown bits on the bottom of the pan.
Add broth, tomatoes and beans; bring mixture to a simmer. Nestle browned lamb shanks into broth mixture; cover and cook until meat is tender and easily falls off the bone, about 1-1/2 to 2-1/2 hours, depending on size of shanks. Place shanks in individual shallow bowls or plates. Divide vegetables and sauce among bowl.
Serve with a simple green salad (arugula or mixed greens dressed with lemon juice and extra virgin olive oil) and whole grain crusty bread.