Preheat oven to 450F
In a large pot over high heat, boil 2 quarts of water. Cook potatoes until tender. Drain well and set aside.
In a medium pan over medium heat, add 1 tablespoon of olive oil, onion, and carrots and cook for 2 minutes. Reduce the heat to low, add the vegetable broth, and cook for 10 minutes.
Meanwhile, pass the potatoes through a vegetable mill (or use potato masher until very smooth). Add vegan butter and non-dairy milk. Season with salt and pepper, to taste. Keep covered and warm.
Add the cauliflower, squash, and beets to the carrot and onion mixture and continue to cook over medium heat for 10 minutes.
Grease a gratin dish and add the vegetable preparation first. Add the mashed potatoes over it and smooth the top with a fork. Sprinkle with vegan cheese. Bake for 7-10 minutes or until golden brown. Serve hot!
This dish can be served all year long. The vegetables can change but should always be seasonal.