Bring the water or vegetable broth to a boil in a large saucepan. Add the cauliflower and cook, covered, for 10 to 12 minutes or until cauliflower is fork tender. Remove from the heat but DO NOT drain.

While the cauliflower is cooking saute the minced garlic with the butter in a small nonstick skillet over low heat. Cook for 2 to 3 minutes or until the garlic is soft and fragrant but not browned (browned or burnt garlic will taste bitter). Remove from heat and set aside.

Puree the creamy cauliflower sauce. Use a slotted spoon to transfer the cauliflower pieces to the food processor. Add 1/2 cup cooking liquid, sauteed garlic/butter, salt, pepper, and milk and half the cheese. Process for for several minutes until the sauce is very smooth, adding more milk to achieve a pourable consistency. Dump any remaining liquid from the pot you used to cook the cauliflower in. Pour the sauce back into the pan and set aside. (You should have about 2-1/2 cups of sauce.)

Slice the potatoes thinly and add them to the pot of creamy cauliflower sauce. Stir to combine. Scrape the potato mixture into the prepared baking dish and spread it out evenly. Sprinkle with the remaining grated Parmesan.

Bake until the top is golden and the potatoes are tender when pierced with a fork, about 1 hour. Remove from the oven and divide into 6 even portions.