Soak the mushrooms in warm water.
Rinse kale, trim, removing the tough central stem. Lay flat and cut into thin strips. Drain the mushrooms and cut into narrow strips. Peel the shallots, chop finely and cook in a pan with the oil until translucent.
Add the mushrooms and sauté until browned and pour in the wine. Add tomatoes, season with salt and pepper and simmer over medium heat for 15-20 minutes.
Preheat the oven to 200°C (approximately 375°F).
Season the sauce again, stir in the parsley and spoon into the bottom of a baking dish to coat thinly.
Top with lasagna sheets, kale strips and another layer of sauce. Repeat this process until the lasagna noodles, kale and sauce are used up, finishing with a sauce layer.
Sprinkle with cheese and bake in preheated oven for about 45 minutes. Serve slices on warmed plates.