Preheat oven to 350 degrees Farenheit. Lightly spray 10x15 deep pan with cooking spray. (I use my roasting pan - it's deep enough) Toss butternut squash with 2 Tbsp olive oil, salt and pepper. Spread on baking sheet, and roast until tender. Puree squash. (That's the "squish) Set aside.
Heat 2 Tbsp olive oil in large non-stick skillet. Saute onions & garlic until fragrant and soft. Add spinach, little bit at a time until all cooked down. Cook until water in spinach evaporates. (That's the Swamp) Set aside.
Mix together the ricotta, egg, parsley, nutmeg, about 1 cup Parmesan cheese, and ½ cup mozzarella cheese. Add salt & pepper to taste. set aside. In 10X15 pan, put about ¾ cup sauce in bottom of pan. Put 3 or 4 noodles to fit. Spread a layer of squash, then "sprinkle" a layer of spinach. Drop by spoonfuls some of the ricotta mix. Spread if you can, trying to keep layers separate. Pour about another ¾ cup of sauce down, then repeat with noodles, squash, spinach, ricotta mix, so you've got 3 layers of the noodles & filling. Top with the remaining noodles, spread more sauce over top all. This will seem much more juicy than a traditional lasagne, but the noodles will absorb a lot of the moisture as they cook.
Cover with foil, put the casserole on a baking sheet, and put in a pre-heated 350 degree oven for 45 minutes. Remove foil, sprinkle with remaining parm and mozzarella cheese, and return to oven until casserole is really bubbly, and cheese is melted and gooey, and lightly browned. Take out of the oven, let sit for about 20 minutes until it cools and "sets" a little more.