Adjust oven rack to lower-middle position and heat oven to 450 degrees. Heat a large heavy roasting pan set over two burners on low heat. Meanwhile, place shanks in a medium bowl with 2 tablespoons oil and turn to coat. Season generously with salt and pepper.

A few minutes before searing shanks, increase heat to a strong medium-high until wisps of smoke rise from pan. Add shanks and sear on all sides until well browned, 7 to 8 minutes total. Transfer to a bowl. Shanks should have rendered enough fat to cook onion. If not, add another tablespoon of oil to pan.

Add onion, carrots, and celery to roasting pan and cook, stirring, until lightly browned, about 5 minutes. Add garlic and herbes de Provence and cook until fragrant, about 1 minute. Whisk in flour, then broth, wine, and tomatoes, and season with salt and pepper to taste.

Return shanks to pan. Using two potholders to protect hands, place a sheet of heavy-duty

foil over pan. Press foil down so that it touches shanks and seal foil completely around edges. Repeat with a second sheet of foil to ensure a tight seal. Continue to cook shanks on medium­high until you hear juices bubble. Set pan in oven and cook for 1½ hours.

Transfer pan from oven to stovetop. Arrange shanks on a serving platter and cover with foil to keep warm. Stir beans into pan juices (remembering that pan handles are hot) and sim­mer over two burners on medium heat to blend flavors, about 5 minutes. Serve.