Add tomatoes, cucumbers, onion, yogurt, garlic, and red wine vinegar in a blender or food processor. Blend at medium to high speed until everything is smooth.
Season with salt, cumin powder, and pepper according to your liking.
Gradually pour in the oil while the blender is running.
Transfer the mixture to a bowl and refrigerate for at least an hour until it is sufficiently cold.
Serve the gazpacho in bowls, and add pieces of burrata on top. Finally, drizzle some oil on top and garnish with fresh basil leaves. Enjoy with bread on the side.