Cut the potatoes into medium sized pieces, place in a medium saucepan, cover with cold water, season with salt, bring to the boil, then simmer until tender.
Meanwhile, make the pesto by placing all the ingredients except the olive oil in a food processor and pulse to form a rough paste. Drizzle in the oil with the motor running.
Bring another medium saucepan filled with salted water to the boil. Cook the broccolini, asparagus and peas until just tender, you may need to do this in batches.
Chop the broccolini and asparagus into small pieces and place in a large bowl with the potatoes and peas.
Pour over the pesto, toss well to combine, season with salt and pepper and serve.
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