1- Top, tail and wash the runner beans, the courgettes and the green beans and cut into pieces, removing any strings if necessary; wash the broccoli florets in cold water and drain; remove the toughest external leaves from the leek, wash and cut into rounds. Blanch the broccoli, the green beans and the runner beans separately in boiling water; drain the vegetables and keep them on one side.
2- Heat the oil in a pan and fry the leek until soft without browning; add the courgettes and fry for 2-3 minutes; add the green beans and runner beans, cover and continue to cook on a medium heat for 7-8 minutes; add the broccoli florets and cook for a further 2-3 minutes and season with salt and pepper. Put the eggs, grated Parmesan cheese, milk and a pinch of salt in a bowl and beat with a fork.
3- In the meantime bring a saucepan of salted water to the boil and cook the pasta, drain and pour into the pan with the vegetables and allow the flavours to blend; remove the pan from the heat, pour in the egg and cheese mixture, season with a pinch of pepper, return to the heat for a few seconds, mix together until the consistency is creamy and then serve.