Preheat the oven to 175°C. Puree the peppers, oregano, tomatoes, 1/4 teaspoon salt, 1/4 teaspoon pepper and the sugar in a food processor or blender until smooth and set aside. Mix 160g of the mozzarella cheese with the egg whites and ricotta cheese in a medium bowl.
Heat the oil in a large nonstick skillet set over medium-high heat. Add the sliced mushrooms and cook, stirring, until they have released their liquid and are tender, about 10 minutes. Stir in the kale, in batches, and as it wilts add the pepper flakes, garlic and 1/4 teaspoon salt and continue to cook until the kale is wilted and bright green, an additional 5 minutes.
Mist a 9-by-13-inch baking dish with nonstick cooking spray. Spread 3/4 cup of the sauce in the bottom of the dish. Top with 3 lasagne sheets, 1/2 of the ricotta mixture and 1/2 of the mushroom mixture. Repeat layers with sauce, lasagne and remaining ricotta and mushrooms. Top with remaining lasagne and sauce. Cover with aluminum foil and bake until the lasagne shets are tender and the sauce is bubbling around the edges of the pan, about 50 minutes.
Uncover, sprinkle with the remaining grated mozzarella and continue to bake until melted, about 5 minutes. Let stand 15 minutes, sprinkle with parsley and serve.