Cut the broccoli vertically into small pieces so that each has flower, stalk and leaf. Blanch very briefly in boiling salted water.
Heat the oil in a large heavy saucepan and fry the garlic gently until light brown. Add the chilli, the anchovies and butter. Mash the anchovies with the garlic using a wooden spoon; they should go creamy. Add the broccoli and the cream, bring to the boil,