1. Cut tomatoes into wedges and place in large bowl. Sprinkle with fleur de sel and pepper. Crush oregano between palms to release flavor; add to tomatoes. Add 1/4 cup basil and olive oil and mix well. Let stand at room temperature at least 30 minutes and up to 1 hour, stirring occasionally.
2. Place 1 burrata cheese round in center of each plate. Fan tomatoes around cheese, dividing equally. Drizzle with dressing from bowl. Garnish with additional basil leaves and serve.