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Heat a large frying pan with the olive oil and boil a large pan of salted water. Add the cubed chorizo to the frying pan and cook for 5 minutes, stirring, until the oils are released into the pan. Halve and finely slice the brussels sprouts. Add these to the frying pan, season and cook for 10 mins, stirring now and then, until tender.
Cook the spaghetti following pack instructions. Whisk the egg yolks, single cream and milk with the grated parmesan and a good grind of black pepper.
When the pasta is cooked, drain, reserving a cup of the cooking water, and add the pasta to the frying pan. Turn the heat to very low and add the egg mixture. Toss everything together for 2-3 mins until the sauce has thickened, adding a splash more water if it looks to dry. Serve with extra parmesan.