1. Preheat the oven to 400 degrees F. Melt the butter in a large nonstick skillet over medium heat. Add the shallots and cook until softened, about 3 minutes. Add the mushrooms and cook until they release their liquid and soften, about 5 minutes. Add the kale and cook until warmed through, about 5 minutes. Season with 1/2 teaspoon salt and a pinch of pepper and set aside.
2. Combine the lasagna noodle pieces with 1 cup water in a large bowl and stir with a rubber spatula. Add the heavy cream and stir until the pieces are evenly coated. Stir in the ricotta cheese, Parmesan, nutmeg, red pepper flakes and 1 teaspoon salt. Add the kale mixture and stir to combine. Pour the mixture into a 9-by-13-inch baking dish and top with the shredded mozzarella
3. Cover the dish with nonstick foil and bake for 35 minutes. Remove the foil and cook until the lasagna is bubbly and slightly browned on top, 15 to 20 minutes. Cool for 30 minutes and serve.