Preheat the oven to 400°F with a rack placed in the center of the oven. Prepare a serving dish by brushing with olive oil. Set aside.
In a large saucepan, heat the olive oil over medium-low heat. Add the shallot and garlic and cook until translucent, about 2-3 minutes. Add the butternut squash, season with salt, and let it brown lightly, cooking for about 4 minutes. Stir in the almond milk. Bring the heat up to medium to let simmer for about 5 minutes, or until the squash is fork-tender. Transfer the butternut squash and milk into a blender and puree until very smooth.
Return the pureed butternut squash to the same saucepan and place over medium-low heat. Stir in 1 cup of the vegan cheese, and adjust the seasoning with salt and pepper. If you find the sauce is too thick, add a touch more almond milk, if necessary.
Spread half of the potatoes into the bottom of the serving dish. Spread half of the cheesy butternut squash sauce over the potatoes, and sprinkle with 1/4 cup of vegan cheese. Top with the remaining potatoes, sauce, and cheese.
Cover the pan and bake for 30 minutes. Remove the foil and bake for another 30 minutes, or until the potatoes are tender and the sauce is bubbling.
Transfer the pan to a cooling rack and serve warm, garnished with parsley.