In the meantime, prepare the béchamel sauce by melting the butter in a small saucepan over a gentle heat, add the flour and stir well with a whisk until the mixture is smooth and lump-free. Pour in the milk at room temperature, stirring well, add a pinch of salt and grated nutmeg and cook over a gentle heat for 5-6 minutes, until it reaches a creamy consistency.
Blanch the broccoli florets in plenty of salted water, drain when soft.