To make the balsamic reduction, pour the balsamic vinegar into a small saucepan. Heat over medium-high heat and bring to a boil.
Reduce the heat to low and let simmer, swirling the pan occasionally, until reduced to about half of the original amount, about 15 minutes. Remove from the heat and set aside.
Meanwhile, place the tomatoes and peaches on a platter or plate. Top with burrata cheese chunks and basil.
Drizzle the balsamic reduction over the salad and serve.