Place the egg yolks, mustard, garlic, anchovies, lemon juice, 2 1/2 teaspoons kosher salt, and 1 teaspoon pepper in a food processor fitted with the steel blade and process for 15 seconds. Combine the olive and canola oils in a glass measuring cup. With the food processor running, slowly pour the oils in a thin stream down the feed tube, as you would to make mayonnaise. Add the grated Parmesan and pulse to combine. The mixture will be thin enough to drizzle on the tomatoes.
Pour a puddle of dressing in the middle of 4 dinner plates. Core the tomatoes and slice crosswise with a serrated knife about 3/8 inch thick. Arrange overlapping slices of tomatoes decoratively on the plates. Sprinkle with the fleur de sel and drizzle more dressing onto the tomatoes with a tablespoon. Sprinkle with the capers, basil, shaved Parmesan, and pepper. Serve at room temperature with a pitcher of extra dressing on the side.
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Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.