• Peel and finely chop the shallots. cut the taleggio cheese into cubes. Wash the radicchio and cut it into thin strips.
• In a frying pan or iron skillet, heat the extra virgin olive oil. Cook the peeled and finely chopped shallots until they start to soften. Add the radicchio and cook for 10-15 minutes over a very gentle heat. Season with salt and pepper. Remove from heat and allow to cool.

Make the béchamel (white sauce)

• Put the butter in a pan over a low heat, melt it, add the flour and mix until it forms a thick paste (roux). Then, remove it from the heat. At this point, slowly add the milk and stir continuously to dissolve the roux without making lumps. Put the pan on a moderate heat and keep stirring constantly until it starts to simmer and thicken.
• Lower the flame. Wait a couple of minutes. Then, turn it off, add a pinch of salt, pepper and nutmeg, mix it again for a few minutes and then allow it to cool to thicken it further. 

Finish the dish

• In a large bowl combine the radicchio, half the grated cheese and the béchamel sauce, mix well and, if necessary, add salt.
• If using dried pasta you will need to bring a pot of bailing salted water to a boil and then blanch the pasta sheets individually. Place them spread apart on a tea towel. Don't allow them to stick together.
• Put a layer of lasagne sheets on the bottom of a greased oven dish. Cover it with a couple of ladles of the béchamel and radicchio mix. Distribute some of the Taleggio cheese pieces onto the radicchio sauce. Sprinkle a little Parmesan or Grana Padano. Then cover with another layer of lasagne. Continue until the ingredients have been used up, ending with a thin layer of radicchio sauce. Sprinkle again with grated cheese and add a few pieces of taleggio. Bake at 180°c degrees.
• Cook for the first 10 minutes covered with aluminum foil and continue cooking for 10-15 minutes uncovered (until the cheese on top is golden). Remove from the oven, allow to cool slightly and serve.