Cook the potatoes in boiling salted water for 10-15 minutes until tender. Drain and halve when cool enough to handle; set aside. Blanch the shelled broad beans and the asparagus in boiling salted water for 2-3 minutes. Drain in a sieve and cool under running cold water. Drain again, fish out the asparagus, then peel off the hard outer skins from the beans – make a nick in the tops and pop the beans out. Blanch the shelled peas in a separate pan for 1 minute. Toss the asparagus, beans, peas, potatoes and prosciutto together.
For the dressing, put all the ingredients in a blender or food processor and blitz until really smooth and bright green. Season with salt and pepper. To serve, toss the salad leaves with a spoonful or two of dressing and arrange on plates. Pile the vegetable mixture on top, season, then drizzle over the remaining dressing and scatter with the pecorino.