Chop the broccoli stalks and set aside. Larger florets can be split in halves or quarters.
Bring a large pot of salted water to the boil and add the pasta.
Boil for 8 minutes (or until very almost cooked through) then add the broccoli florets.
Cook until the broccoli is tender and the pasta is cooked. Reserve 1 cup of cooking water and drain.
In a large pan, melt butter or add a few tablespoons of olive oil. Add the garlic and broccoli stems and cook for a few minutes.
Pour in the cream, lemon juice and zest and season. Allow to simmer for a few minutes until the sauce has thickened slightly and coats the back of a spoon easily.
Tip the drained pasta and broccoli into the sauce and add a splash of pasta cooking water. Toss to coat in sauce, adding more pasta water if necessary.
Add a generous amount of grated cheese, toss and serve.