In a large bowl, gently toss the tomatoes with 2 tbsp. vinegar to coat. Add the torn basil and 2 tbsp. EVOO. Season with salt and pepper and toss again.
Divide the tomato mixture among 8 plates. Top each with 1 burrata half. Drizzle with the remaining 2 tbsp. EVOO and sprinkle with salt and pepper. Garnish the plates with the basil sprigs. Drizzle the remaining 2 tbsp. vinegar over the salads. Serve immediately.