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Heat the grill to high. Put the broccoli on a baking tray and drizzle over 1 tsp of the oil. Season, and toss together. Grill for 8-10 mins, tossing around halfway through, until crispy and charred.
Cook the pasta in salted water following pack instructions. Drain, reserving a cup of the cooking water.
In a frying pan, heat the remaining 2 tsp oil over a medium heat, and fry the garlic, walnuts and chilli for 3-4 mins until golden.
Tip in the pasta, broccoli, lemon zest and juice, reserving a little of the zest. Add a splash of the reserved cooking water and toss everything together to coat the pasta. Serve in warmed bowls with the remaining lemon zest scattered over.