Let the radicchio cool. Set aside half. In a separate bowl, add the flour to the cold milk and mix well to remove any lumps, then add half of the cooked radicchio.

Cook the mixture until it thickens. Add nutmeg and black pepper to taste. Assemble the lasagna by layering radicchio, lasagna noodles, the radicchio béchamel, and thin slices of cheese as desired.

Sprinkle with grated cheese and a pinch of chili powder. Bake at about 350°F (180°C) for 30 minutes.