Put a large pan of water on to boil, salt it lightly, then add the broad beans and let them cook for 5 or 6 minutes until tender. Remove the beans with a draining spoon or kitchen spider then bring the water back to the boil and add the peas
If your beans are young and very small, you can leave them as they are. If they are on the larger side, then you might like to remove their pale outer skins. Drain the peas in a colander and set aside with the beans.
Pull the leaves from the basil and put them into the jug of an electric blender. Pour in the olive oil, water, sugar and a little salt, then process to a thick, green dressing. Stir into the peas and beans.
Break open the balls of burrata and place one each on 2 plates or shallow dishes. Spoon some of the peas, beans and their dressing over the burrata just before you bring them to the table.