Preheat grill to medium-high heat.
Make the pistachio herb vinaigrette. Chop the pistachios and basil. Combine with 2 tablespoon balsamic vinegar, 2 tablespoon lemon juice, 1 teaspoon dijon mustard, and ¼ cup olive oil. Season with salt and pepper.
Toss the cut peaches in 1-2 tablespoon olive oil. Grill the peaches until grill marks appear, about 4-5 minutes. Flip and grill on the other side until grill marks appear, about 4-5 minutes. Remove from heat.
Heat 1 tablespoon oil in a saute pan. Saute the corn kernels until slightly charred, slightly occasionally. Season with salt.
Assemble the salads. Arrange the grilled peaches on a plate followed by the sauteed corn, cherry tomatoes, fresh mozzarella, and shallots. Drizzle extra virgin olive oil on top and season with salt and pepper. Sprinkle fresh basil and mint on top and serve with the raspberry balsamic vinaigrette.