Combine all the dressing ingredients in a jar or small bowl, shake or whisk together, and set aside.
In a serving bowl, add the sliced grape tomatoes and peach wedges. Use 1/2 of the dressing and pour over the sliced tomates and peaches. Gently toss to combine.
Top the tomatoes and peaches with burrata and gently pull the burrata apart with two forks.
Spoon desired amount of extra dressing over the pulled burrata.
Garnish with fresh basil and serve immediately.