First do all your slicing. Slice your mushrooms, squash and zucchini in thin strips lengthwise. Be sure to wash all veggies in cool water after slicing to help them stay moist while you work.
Preheat oven to 475°F.
Over medium high heat, sauté sausage with 2 teaspoons of extra virgin olive oil.
Once most of the meat is done, add all the mushrooms to the pan and cook only until meat is done. Do not over cook or your mushrooms will over cook! (This is important because you'll need some juice still in your mushrooms for lasagna since we are not using a lot of sauce).
Mix all your cream ingredients together in a food processor or blender, whichever you choose, until it is smooth. Set to the side and begin assembling.
Lightly grease a casserole dish with olive oil and sprinkle 1/2 cup of Parmesan cheese on the bottom of dish. This will make a nice crust on the bottom. Begin to layer your squash along the pan and be sure to cover the bottom as well as possible. There will be a little space between, but don't worry about it.
Spoon out half your meat and mushroom mixture on top of squash. Now spread half your cream mixture on top of meat and mushrooms. Then sprinkle half your bag of shredded cheese on top of that layer. Repeat all this steps again for your second layer.
Wrap the dish in foil and place in the oven for 45 minutes. Remove from oven after 45 minutes and remove foil. Lasagna will be a little loose because squash and zucchini render a lot of juice. Place in oven for another 15 minutes uncovered. After 15 minutes remove from oven and allow at least 20 minutes for it to cool and firm up. This takes less time than you think, but even the cooking and cooling time is well worth the wait!
After it cools and some of the liquid is gone sprinkle with some fresh or dry herbs, slice and enjoy! (I didn't use salt because I find the the sausage is plenty).