Heat up a deep pot filled with water and add it a handful of coarse salt. Cover and bring to a boil.
Clean the mushrooms and cut them into chunks.
Put in a pan or wok finely chopped garlic, a drizzle of olive oil and add in the sliced mushrooms. Season with salt, pepper and fresh thyme leaves to taste. Cover with a lid and simmer on low heat until the mushrooms are tender and their water has dried out.
Uncover the mushrooms, add them radicchio cut into thin strips and let them simmer for a while, until the radicchio leaves are done.
Turn off the heat and set the vegetables aside.
Put the lasagna sheets in the pot with boiling water, mix well and let simmer uncovered for 6 minutes.
Place next to the pasta pot a large bowl and fill it with cold water and a handful of coarse salt.
Prepare now the sauce: blend together with an immersion blender ricotta cheese and vegetable stock. You'll have to get a soft, smooth sauce; the broth you will need may vary according to your ricotta cheese dryness.
Season the ricotta "besciamella" sauce with salt, pepper and plenty of grated nutmeg.
Preheat the oven to 350°F.
Drain the pasta sheets, place them in the bowl with cold salted water and let them cool down. Take the pasta sheets one by one and place them on a clean kitchen towel, so they can dry better.
Take a baking dish and grease it lightly with olive oil; start composing the lasagna putting a bottom layer of pasta, besciamella ricotta sauce, mushrooms and radicchio and finally sprinkle with grated ricotta.
Continue with the layers in the same way, taking into account that you have to top the lasagna with besciamella and grated ricotta cheese only.
Bake the mushroom and radicchio lasagna for 20 minutes.
Turn on the grill and bake 5 minutes more, serve immediately.
The recipe can be made lactose-free and vegan by substituting fresh ricotta cheese with soy and the seasoned with vegetable substitutes Parmesan (nutritional yeast flakes and / or ground almonds).
This lasagna can be made lactose-free and vegan by substituting fresh ricotta cheese with silk tofu and seasoned ricotta with nutritional yeast flakes and ground almonds.