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Pat lamb shanks dry and season with 1/2 tsp salt and 1/4 tsp pepper. Heat oil in pressure cooker over medium-high heat until it shimmers, then brown shanks well, 1 at a time, transferring to a plate.
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Add onion, carrots, celery, and garlic to pressure cooker and sauté until golden brown, about 6 minutes. Add tomatoes with juice and rosemary and cook, stirring, 1 minute. Stir in beans, water, 1/2 tsp salt, and 1/4 tsp pepper.
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Return lamb shanks to pressure cooker and bring to a boil. Seal lid and cook at high pressure according to manufacturer's instructions, 30 minutes. Put pressure cooker in sink (do not remove lid) and run cold water over lid until pressure goes down completely. Remove lid and discard rosemary, then transfer shanks to a cutting board and coarsely shred meat.
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Spoon bean and vegetable mixture into large shallow bowls, then top with lamb and sauce.