This tasty meal can be made with store bought pasta sheets or with your favorite homemade pasta recipe. Replace the chicken stock with vegetable broth for a delightful vegetarian option.
Melt the butter in a saucepan over medium heat. Add the flour and cook three minutes, stirring with a wooden spoon so the flour colors but doesn’t brown. Gradually add the hot milk, whisking. Add vegetables. Bring to a boil. Stirring constantly, cook until thick, about 8 minutes. Salt to taste, white pepper to taste and add nutmeg. Let sauce steep off heat with vegetables and bay leaf to become more flavorful.
Cook the Pasta
Cut the sheets of pasta into 4x2-inch rectangles. In a large saucepan of boiling salted water, cook half of the pasta rectangles, stirring constantly, until barely tender, about 30 seconds. With a slotted spoon remove the pieces and place them in a large bowl of cold water. Repeat with the remaining pasta rectangles. Remove each piece of pasta separately from the bowl and drain on paper towels (or cook lasagna noodles according to package instructions).
Prep the Radicchio
Preheat the broiler. Remove the tough outer leaves from the radicchio and cut out the cores. Separate the leaves. Working in batches, cover a large baking sheet or jelly-roll pan with radicchio leaves and drizzle 2 Tbsp of olive oil over the leaves. Turn to coat. Broil the leaves 6 inches from the heat until lightly browned, about 2 minutes (the radicchio will shrink as it cooks). Repeat in 3 more batches with the remaining radicchio. Stack the leaves in piles and cut into 1/2-inch strips.
In a large skillet, heat the remaining 1/2 cup olive oil. Add the shallot and garlic and cook over moderate heat until fragrant, about 30 seconds. Add the radicchio and chicken stock. Reduce the heat to low and simmer until the radicchio is tender and the stock has almost evaporated, about 10 minutes. Season with salt and pepper.
Preheat the oven to 350°F. Butter a large shallow rectangular baking dish that will hold half the pasta rectangles in a single layer (if necessary, use two baking dishes, one larger and one smaller). Using a slotted spoon, remove the large pieces of vegetables and the bay leaf from the béchamel sauce. Spread 1 cup of the béchamel sauce over the bottom of the baking dish.
Place 3/4 cup of the Parmesan cheese on a plate and dredge each pasta rectangle in the cheese to coat both sides. Arrange a single layer of cheese-coated pasta over the béchamel. Spread the radicchio on the pasta and arrange the mozzarella slices on top. Spoon 1 cup of the béchamel sauce over the mozzarella. Dip the remaining pasta rectangles in the Parmesan and cover the filling with the pasta. Spread the remaining béchamel sauce over the top. Sprinkle on the remaining 1/2 cup Parmesan cheese and drizzle the melted butter over all.
Bake in the middle of the oven for about 30 minutes, until the top is golden brown.