Heat a large frying pan over a medium heat. Peel the whole garlic cloves and fry them along with the chorizo for 5-7 mins, or until the chorizo turns crisp at the edges. (You won’t need any oil as the chorizo will release its own.) Scoop out the garlic with a slotted spoon and discard.

Whisk the eggs and egg yolks in a bowl. Add the parmesan, a pinch of salt and some black pepper.

Cook the spaghetti in a large pan of boiling salted water for 5 mins, then add the broccoli and cook for a further 2 mins. Drain, reserving some of the pasta cooking water. Add the spaghetti and broccoli to the frying pan with the chorizo, then quickly pour over the egg mixture and toss quickly to coat. Add a splash or two of the reserved cooking water to loosen, if needed, then serve in four shallow bowls.