Lady pea and mixed heirloom tomato salad

3 cups shelled lady peas or other delicate field peas;

4 tablespoons extravirgin olive oil, divided;

Kosher salt and ground black pepper;

3⁄4 cup high-quality mayonnaise;

2 teaspoons finely grated lemon zest;

2 tablespoons fresh lemon juice;

1 large garlic clove, finely chopped;

2 cups ripe cherry or other miniature tomatoes, left whole or halved, depending on size;

2 tablespoons finely chopped sweet onion or shallot;

1 tablespoon sherry vinegar;

1 tablespoon finely chopped flat-leaf parsley;

2 to 3 large heirloom tomatoes, cored, peeled if necessary, and cut into a total of 12 slices;

12 large basil leaves.

Bring a large saucepan of water to a boil. Add 1⁄2 teaspoon kosher salt per cup of water. Stir in the peas, reduce the heat, and simmer until just tender, about 15 minutes. Skim off any foam. Drain, transfer into a large bowl, and stir in 2 tablespoons of the oil. Season with salt and pepper, cover, and refrigerate until chilled.
Whisk together the mayonnaise, lemon zest, lemon juice, and garlic in a small bowl. Cover and refrigerate until chilled.
Stir the cherry tomatoes into the field peas. Stir in the onion, vinegar, and parsley and the remaining 2 tablespoons of oil. Season generously with salt and pepper.
To serve, divide the tomato slices among the serving plates and tuck the basil leaves around them. Spoon the tomato and pea mixture over the slices. Top each serving with a generous spoonful of the mayonnaise mixture. Serve at once.
Make-ahead note: The peas can be cooked up to 1 day ahead; store covered and refrigerated. The mayonnaise mixture can be made up to 1 day ahead; store covered and refrigerated.