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1
Put turkey breast in a 6- to 8-quart pasta pot and add broth and enough water to cover turkey by 1 inch.
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2
Remove turkey and bring liquid to a boil.
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3
Season with salt and return turkey to pot, then poach at a bare simmer, uncovered, skimming any froth, until an instant-read thermometer inserted 2 inches diagonally into thickest part of breast (do not touch bone) registers 155F, 1 to 1 1/4 hours.
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4
Cool turkey in broth 30 minutes (internal temperature will rise to 170F).
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5
Puree tuna, anchovies, mayonnaise, oil, lemon juice, and water in a blender until very smooth.
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6
Transfer turkey to a cutting board, then bring remaining poaching liquid to a boil.
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7
Add half of beans and cook, uncovered, until crisp-tender, 3 to 5 minutes.
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8
Transfer with a slotted spoon to a colander and refresh under cold water.
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9
Cook remaining beans and refresh in same way.
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10
Add potatoes to broth in pot and simmer until just tender, about 10 minutes.
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11
Drain potatoes, reserving broth for another use.
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12
Thinly slice turkey breast on the diagonal.
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13
Arrange beans on a platter and top with potatoes, then drizzle vegetables with some tonnato sauce.
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14
Top with turkey slices and more tonnato sauce.
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15
Sprinkle dish with capers, olives, and basil.
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16
Serve remaining sauce on the side.
