Bring a pan of water to the boil and salt it lightly. Tip in the peas and let them cook at a rolling boil for 3 or 4 minutes till bright and tender, then drain them.
Put the basil into a blender with the olive oil and vinegar, and reduce to a bright green dressing. Transfer to a bowl and add most of the warm, freshly drained peas. Set the others aside.
Put the burrata on a serving dish and squeeze them until they split open. Spoon the pea and basil dressing over them. Scatter over the reserved peas and small basil leaves and serve.