Jean Lentz, David's mother, has always made this salad with big red beefsteaks, but a combination of heirloom tomatoes of different colors, sizes and shapes is especially pretty. If you prefer, you can serve the salad immediately, without chilling it.
In a medium bowl, combine the shallots and garlic with the vinegar and 1 teaspoon of salt and let stand for 5 minutes. Add the lemon juice and season with pepper. Crush the basil sprigs in your hands to release their flavor, breaking them up a little, and add them to the bowl. Whisk in the olive oil and let stand for 10 minutes; discard the basil sprigs.
Spoon one-quarter of the vinaigrette onto a large shallow platter. Arrange half of the tomato slices in overlapping circles on the platter and season with salt and pepper. Using a sturdy vegetable peeler, shave half of the provolone over the tomatoes. Spoon half of the remaining vinaigrette on top and sprinkle with half of the chopped basil. Repeat with the remaining tomatoes, cheese, vinaigrette and basil, seasoning with salt and pepper between layers. Cover with plastic wrap and refrigerate for 2 hours before serving.