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Using a sharp
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or
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, slice off the very bottom of the tomato. Place a box grater in a medium bowl. Rub cut face of tomato over large holes of box grater, using the flat palm of your hand to move the tomato back and forth. The flesh should be grated off while the skin remains intact in your hand. Discard skin and season tomato pulp lightly with kosher salt to taste. Transfer tomato pulp to a
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and set aside along with the bowl (no need to wash it).
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Place egg, lemon juice, anchovies, mustard, and capers in the bottom of an immersion blender cup or another tall-sided container that just fits the head of your immersion blender. Pour vegetable oil on top and allow to settle for 15 seconds. Place head of immersion blender at bottom of cup and turn it on high speed. Do not pulse or move the head. As mayonnaise forms, slowly tilt and lift the head of the immersion blender until all oil is emulsified; this should take between 30 and 45 seconds.
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Turn off blender and remove from blender cup. Scrape down sides of cup using a rubber spatula, then add tuna, 2 tablespoons (30ml) reserved tomato pulp, and pepper paste. Return blender head to blender cup and blend just until ingredients are thoroughly incorporated into a smooth sauce, 15 to 30 seconds.
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Taste sauce and adjust the level of heat to your liking with more pepper paste. Check the consistency of the sauce as well; it should be looser than regular mayonnaise, but still thick enough to coat a spoon (somewhere between creme fraiche and stirred whole-milk yogurt). Gradually blend in remaining tomato pulp, stopping if the sauce starts to get too runny; reserve any remaining pulp. Avoid over-blending the sauce, as this can cause it to become grainy.
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Transfer sauce to reserved bowl and slowly drizzle in olive oil while whisking constantly to emulsify. Season to taste with kosher salt. Refrigerate sauce until ready to serve.
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Using a sharp chef's knife or serrated knife, cut tomatoes into an assortment of slices, wedges, and bite-size pieces.
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Using a large spoon, spread tonnato in an even layer on a large serving plate or individual serving plates. Arrange tomatoes on top of tonnato and spoon any remaining tomato pulp over them. Sprinkle sesame seeds and sea salt (if using) over tomatoes, followed by basil leaves. If not using sea salt, season tomatoes with kosher salt. Serve immediately.
