Cook your pasta sheets in hot water. Follow the package directions closely. Drain the water out well.
Heat your sauté pan over medium-high heat. Add your olive oil to the pan. Toss in your mushrooms and garlic.
Cook the mushroom mixture for five minutes. Stir until they look tender. Set them aside to cool.
Turn your oven to 350 degrees now. Spray your deep baking dish well. Use your favorite non-stick cooking spray.
Grab your large mixing bowl. Combine your cheeses, cream, basil, and seasonings. Stir in the eggs and mushrooms.
Spread half a cup of cheese mixture on the bottom. Lay down five pasta sheets. Add two cups of cheese mixture.
Place half of your squash and zucchini ribbons down. Top with six mozzarella slices. Sprinkle one cup of Italian cheese.
Repeat all the layers one more time. Finish with a final layer of pasta, cheese, and mozzarella.
Cover the baking dish tightly with aluminum foil. Bake it in the oven for one hour.
Remove the shiny foil carefully. Bake for twenty more minutes until brown. Let it cool before slicing.