Preheat the oven to 375F; brush the inside of an 8 by 8-inch casserole dish with oil.
Add the sliced butternut to a 5-quart pot and add water so the pot is 3/4 full. Bring to a rolling boil, and boil 1 minute, 30 seconds, turning the heat down slightly so it doesn’t boil over. Turn off the heat and let the butternut sit in the hot water for 30 seconds, and then drain the squash well. Set aside for now.
Meanwhile, make the creamy white sauce. To do so, heat the oil in a large, deep-sided skillet over medium heat. Add the onion and cook until softened and starting to caramelize, about 5 to 7 minutes, stirring occasionally. Add the garlic and cook 30 seconds more, stirring constantly. Stir in the cream cheese, almond “milk”, salt, black pepper, and nutmeg. Bring to a simmer, stirring constantly, and then turn off the heat and stir in the parsley.
To layer the lasagna, arrange slices of butternut in the bottom of the prepared dish in an even layer; spread on 1/3 of the white sauce and top with 1/3 of the sliced cheese. Repeat these layers 2 times. Sprinkle the remaining 1 teaspoon parsley on top.
Cover the dish with foil and bake until bubbling throughout, about 1 hour.
Serve hot, along with parmesan grated topping if desired.