Put a saucepan with plenty of water in it on to boil. Wash the broccoli, cut the florets off the stalks and rinse again. Peel the potatoes, wash them and cut them into large pieces. When the water comes to the boil, add salt, drop in the potatoes and, after a couple of minutes, the broccoli florets. Cook for 10-15 minutes (test with a fork to see if they are cooked), strain the vegetables “al dente” – they mustn’t overcook. Now prepare the béchamel sauce: Put the butter in a small (heavy-bottomed) pan over a low heat. As soon as it has melted, add the flour and stir for 2-3 minutes with a wooden spoon, without letting the mixture brown. In the meanwhile bring the milk to the boil. Pour a small amount of boiling milk into the saucepan and mix thoroughly; gradually add all the milk, stirring constantly. Cook for approximately 10 minutes, over a very low heat, taking care that the sauce doesn’t stick to the bottom of the pan. Turn the heat off, season with salt and nutmeg,  add half of the grated pecorino cheese and stir well. Grease a baking tin with butter, spread a few spoonfuls of béchamel sauce over the bottom, distribute the vegetables on top, then cover with the resto of the béchamel. Level the surface, but leave a few broccoli florets sticking out: this looks good because it give the dish a touch of colour. Mix the remaining pecorino with the breadcrumbs and sprinkle over the surface. Bake in a preheated oven, at 200 °C, for 20-25 minutes.