Marinate the lamb rumps. Place the pared lemon zest and juice in a bowl. Add the lamb, rosemary and garlic, then cover and leave at room temperature for 1 hour, turning the rumps in the marinade a few times. Then, add the olive oil and salt & pepper.
Preheat the oven to 180°C/160°C fan/Gas Mark 4.
Make the polenta. Pour 1 litre of water into a saucepan. Place over a high heat and, when the water comes to the boil, very gradually whisk in the polenta. Then reduce the heat and cook for 30 minutes, until it no longer sticks to the side of the pan.
Add the olive oil and salt and leave to one side to keep warm. Meanwhile, make the sauce. Heat a saucepan over a medium heat and add the olive oil, garlic, anchovies and parsley.
Cook gently for 2 minutes, then add the olives, cook for 1 minute, then add the cream. Bring to a simmer and turn off the heat. Leave to one side to keep warm.
For the broccoli, bring a pan of salted water to the boil. Add the broccoli, including any leaves, and bring back to the boil. Boil for 2 minutes, then remove from the heat and drain, keeping the hot pan.
Add 2 tablespoons of olive oil and the sliced garlic to the pan and cook over a medium heat for 1 minute. Add the broccoli, and cook for 10 minutes, until broken up slightly.
Check the seasoning and add a tablespoon of water and the remaining tablespoon of olive oil. Stir to coat, and leave to one side to keep warm.
Cook the lamb. Pat off the marinade residue from the lamb using kitchen paper. Season the meat with salt and pepper.
Heat 1 tablespoon of olive oil in a large, ovenproof frying pan over a medium heat. Seal the lamb rumps, turning to brown on all sides (this should take 4 minutes).
Place the lamb rumps fat-sides downwards in the pan then roast in the oven for 8 minutes. With a meat thermometer, check that the middle of the lamb is 45°C for nice pink meat, then remove from the oven. Turn them over a couple of times and leave to rest.
To serve, spoon the polenta onto a serving dish then top with broccoli. Against the grain, slice each lamb rump into 3 slices and place on top of the broccoli and polenta. Pour over the sauce and serve immediately.