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In a large pan, heat the oil and cook the sausageballs until golden, moving them around in the pan frequently. Meanwhile, mix together the eggs, cheese and some seasoning with a fork in a jug.
Cook the pasta following pack instructions. Add the broccoli for the final 3 mins, then drain, reserving a cup of the cooking water.
Add the garlic to the sausageballs and cook for a couple mins more, being careful the garlic doesn’t brown. Remove the pan from the heat.
Add the pasta and broccoli to the sausage pan. Toss everything together, then add the egg mixture. Stir the sauce through the pasta for 1-2 mins. The heat from the pan will cook the sauce – if it is too thick, use a little of the reserved cooking water to thin it. Divide between pasta bowls and serve with extra Parmesan, if you like.