Halve the stone fruits and remove the pits. Dice into 1" pieces and place into a salad bowl.
Halve and/or dice the tomatoes into 1" pieces and toss into the bowl with the diced stone fruit.
Top the stone fruits with the fresh basil leaves, salt, and a pepper. Toss.
Divide the salad between four plates. Nestle a piece of burrata cheese into each salad. Drizzle each salad with half a tablespoon of extra virgin olive oil and serve immediately.