1. Preheat the oven to 210°C (410°F).
2. Cut the florets of the broccoli and cauliflower.
3. Clean them and put them in a large pot filled with water.
4. Place the pot over medium heat and bring to a boil.
5. Once boiling, blanch the broccoli and cauliflower florets for 15 minutes.
6. Meanwhile, melt the butter in a saucepan over low heat.
7. Add the flour all at once and mix well until you get a roux.
8. Then, gradually pour in the milk while whisking continuously, and let it cook until the béchamel sauce is smooth and thick.
9. Remove the saucepan from the heat and add the powdered nutmeg. Season with salt and pepper, then stir well.
10. When the broccoli and cauliflower florets are cooked, drain them well in a colander.
11. Grease a gratin dish and pour the vegetable florets into it.
12. Cover with half of the grated cheese, the béchamel sauce, and then the remaining grated cheese.
13. Bake for 20 minutes.
14. After removing from the oven, let the broccoli and cauliflower gratin rest for 5 minutes on a cooling rack.
15. Serve it in plates and enjoy while it's still hot.
16. Serve with fish.