Sprinkle shanks with kosher salt. Pour olive oil into a 6- to 8-quart ovenproof pan or a 13- by 16-inch roasting pan over medium-high heat. When hot, add shanks in a single layer (work in batches if necessary). Cook, turning until richly browned on two sides, 10 to 12 minutes total; transfer to a plate.
Add wine and vinegar and bring to a boil; cook until liquid is almost evaporated, stirring to loosen browned bits, 5 to 8 minutes. Add vegetables, ginger, 3 tablespoons thyme, bay leaves, pepper, tomato paste, garlic, orange and lemon peels, broth, and shanks. Cover pan (with foil if using a roasting pan).
Bake in a 325° oven until meat is very tender when pierced, 2 1/2 to 3 hours.
Meanwhile, in a 5- to 6-quart pan over high heat, bring 3 quarts water to a boil. Add beans; cook until crisp-tender to bite, 1 to 2 minutes. Drain, place in ice water until cool, and drain again.
With tongs, transfer shanks to a plate; cover with foil. Remove bay leaves and skim fat from pan. Working in batches, purée liquid and vegetables in a blender.
Melt butter in a 10- to 12-inch pan over medium-high heat. Add beans, grapes, sage, and remaining thyme; stir until hot, 3 minutes. Place each shank in a bowl; top with sauce and bean mixture.