Coarsely chop the pistachios and roast them in a pan. Clean and wash the sugar snap peas. Clean and wash the broccoli and cut into florets. Wash lemon hot, dry, finely grate peel. Squeeze the lemon.
Cook the pasta in 4-5 l boiling salted water (1 teaspoon salt per litre) according to the instructions on the packet. Cook half broccoli in boiling salted water for about 5 minutes. Quench cold and puree finely. Mix with pesto, lemon peel and juice. Season to taste with salt and pepper.
Cook the rest of the broccoli and sugar snap peas in the pasta water for about 4 minutes. Drain, mix with pesto, arrange and sprinkle with pistachios.