
In a shallow serving bowl, combine the peaches, arugula and basil. Add 1 tablespoon of the olive oil and 1 teaspoon of the vinegar, and stir to combine all of the ingredients.
Gently tear open each ball of burrata and nestle them into the center of the peach mixture. Drizzle the burrata with the remaining 1 teaspoon olive oil and 1 teaspoon balsamic vinegar. Sprinkle the pistachios all over the dish, followed by some reserved basil leaves, plus a sprinkle of black pepper. Sprinkle a pinch of flaky salt over the cheese, if using.
Serve with crostini or crusty bread on the side, if using. This dish is best the day it’s made, but leftovers are good for several days in the refrigerator, covered.