Begin by making the basil dressing. In small food processor, blend together all ingredients until smooth, scraping down the bowl once or twice as you go. You may need to tip the processor slightly on its side if there’s not enough liquid to run it upright. You can also put the ingredients in a small bowl with tall sides and use an immersion blender to blend. Or, feel free to finely chop the basil leaves and whisk all the ingredients together.
Next, shell and chop pistachios, and set aside.
Slice peaches and tomatoes into wedges, and lay out on a large platter overlapping slightly.
Either leave burrata intact and place in the middle of the platter, or break up into small chunks and scatter over the peaches and tomatoes.
Drizzle with the basil dressing.
Sprinkle chopped pistachios on top, then season with cracked black pepper and coarse sea salt to taste.
Notes
This dish is best made right before you want to serve it. It doesn't refrigerate well, and the peaches will start to brown fairly quickly as they sit. You can make the basil vinaigrette a little bit in advance, but that too will discolor a bit if you leave it overnight in the refrigerator. If you must make it ahead of time, press a piece of saran wrap on top of it to help it keep its vibrant green color. Ingredient Notes
Peaches: I love to use white peaches for this dish, but you can also use yellow peaches. If you hate peach skin, you can remove it before you slice the peaches. If you don’t have peaches, try nectarines. Or just leave them out for a more classic caprese with just tomatoes.
Tomatoes: Choosing ripe, local, farm-grown tomatoes will give you the best flavor for this dish. Use large beefsteak tomatoes for this dish if you can, though you could also try with cherry tomatoes.
Burrata: Obviously it’s not a burrata caprese if you replace the burrata, but you could definitely substitute fresh mozzarella cheese for the burrata if that’s easier to find.
Pistachios: Pistachios add texture and give this dish an appealing crunch. Replace with chopped almonds or hazelnuts for a similar crunch but different flavor.
Coarse sea salt: I love a coarse sea salt like Maldon to sprinkle over the top of this dish, but if you don't have any, feel free to replace with regular sea salt or kosher salt.