Finely dice the onion, garlic and ham, divide the broccoli into florets. Heat the olive oil in a pan and sauté the onion and garlic. Add the broccoli and pour the cream and milk on top. Let the broccoli simmer gently depending on how firm the broccoli is.
In the meantime, put the pasta on. Put the cooked pasta in the pan and season with salt and pepper.