Preheat the oven to 375° F.
To make the filling, put the beans, pine nuts (cashews or hemp seeds), nutritional yeast, miso, lemon juice, basil, garlic, and red chile flakes in a food processor fitted with the “S” blade and process until smooth. Add the spinach or kale and process until well incorporated.
In a large nonstick sauté pan, sauté the onion in 2 tablespoons of water until translucent, about 8 minutes, adding more water 1 tablespoon at a time, if necessary, to prevent sticking. Add the mushrooms, tamari, and garlic and sauté until the mushrooms are browned. Taste and add more garlic or tamari as desired. Cook until the mushrooms look glazed and there is no more liquid left in the pan.
To assemble the lasagna, pour 3 cups of marinara sauce into the lasagna pan or a 9x13 pan. Place one layer of the noodles on top of the sauce. Cover the noodles with half of the bean mixture, then cover the bean mixture with half of the mushroom mixture. Place another layer of noodles over the mushroom mixture and top with the remaining bean mixture followed by the remaining mushroom mixture. Place one more layer of noodles on top of the mushroom mixture and evenly cover with the remaining marinara sauce.
Sprinkle the olives over the top and dust liberally with Faux Parmesan.
Bake uncovered for 1 hour. Let rest for 10 minutes before slicing and serving.