Preheat your oven to 375°F (190°C). Place your cauliflower in a baking pan or a Dutch / French oven with a lid that will close over it. I use a Staub cast iron cooking vessel with a glass lid but you can use a baking pan and cover with foil.
Fill your cooking vessel with a little water (just enough to cover the bottom) and drizzle the cauliflower with a little olive oil and sprinkle with salt and pepper. Cook, covered, for 40 minutes.
While your cauliflower is cooking, fill a cooking pot with water and salt generously. Add your yukon golds whole with skin on, and bring to a boil. Boil until fully cooked and tender inside, about 30 minutes.
When your potatoes are cooked, remove from the water and allow to cool enough to be handled. Remove the skins with your hands, and set aside.
Cut your cauliflower into manageable pieces (it should be very soft now) and place with the peeled potatoes.
Using either a stand mixer (I use the whisk attachment), a food mill, or a potato masher, mash both the potatoes and the cauliflower and mix. Add your vegan butter, non-dairy milk, and garlic powder. Mix well until creamy. Add salt and pepper to taste, and serve immediately.