Lay out the tomato slices decoratively on a serving platter.

Blend all the ingredients for the tonnato sauce in a blender until absolutely smooth. The mixture should be thick but pourable; if not, add a bit more lemon juice. Taste and adjust for salt, although it shouldn't need much. See our post on vitello tonnato for detailed, step-by-step instructions using homemade mayonnaise (see Notes for link).

Pour the sauce over the tomato slices and around the sides. Unlike when making vitello tonnato, you don't need to be careful to cover all the tomatoes with the sauce. In fact, it's nice to leave some exposed for color.

Sprinkle the top here and there with some capers and the minced parsley. Decorate with basil leaves if you like for more color. Serve immediately.