Preheat the oven to 180°C (350°F/Gas 4) and grease a 1 litre(35 fl oz/4 cup) shallow ovenproof dish that is suitable to take directly to the table. To make the béchamel, melt the butter in a small saucepan. Whisk in the flour and cook for a few minutes, stirring constantly, then begin adding the warm milk. It will be immediately absorbed, so work quickly, whisking with one hand while adding ladlefuls of milk with the other. When the sauce seems to be smooth and not too stiff, add salt, pepper and a grating of nutmeg and continue cooking, even after it comes to the boil, for 5 minutes or so, mixing all the time. It should be a very thick and smooth sauce.
Meanwhile, bring a saucepan of salted water to the boil and cook the broccoli for a few minutes until it has softened a little but is still bright green. Lift out with a slotted spoon, letting the water drain off, and put it in the oven dish. (Save the broccoli water for cooking rice or pasta, or adding to a roast instead of water.)
Stir the parmesan into the béchamel sauce and pour over the broccoli, leaving some florets still showing. Bake for about 30 minutes and then serve hot.