In a large pot, combine 1 tablespoon of the vegan butter, the minced garlic, 1 teaspoon of the salt, ½ teaspoon of the pepper, and 3 cups water. Bring to a boil. Add the polenta and stir until the water has been absorbed, 1 to 2 minutes. Remove from the pan and spread the polenta over a baking sheet; let cool in the refrigerator.
Remove the cauliflower stem, coarsely chop it, and place it in a food processor. Pulse seven or eight times, or until it is finely minced, similar to the size and consistency of grains of rice. Divide the cauliflower into two equal portions.
Fill a large pot with water and add half the cauliflower, the whole shallots, and the garlic clove. Bring to a boil, and boil for 20 to 25 minutes, or until the cauliflower is soft. Drain the water and transfer the boiled cauliflower, shallots, and garlic to high-speed blender. Blend until smooth.
In a large sauté pan, heat 2 tablespoons of the olive oil over medium-high heat. Add the chopped shallot and sauté for 1 to 2 minutes, then add the rest of the minced cauliflower and stir well. Add the white wine and sauté for 1 to 2 minutes, then add the pureed cauliflower and stir. Add 1 cup water, ½ teaspoon salt, and 2 tablespoons of the vegan butter and stir. Add the parsley and stir to combine.
In a medium skillet, heat 2 tablespoons of the olive oil over medium-high heat. Add the mushrooms and a pinch each of salt and pepper. Sauté until the mushrooms begin to brown. Set aside.
Remove the polenta from the refrigerator and use a large thin-rimmed glass or a cookie cutter to cut it into rounds.
In a separate medium sauté pan, heat the remaining 1 tablespoon of olive oil over medium heat. Add the polenta cakes and sauté for 1 to 2 minutes on each side, or until golden brown on both sides.
To assemble, divide the polenta cakes between two plates, then top with the cauliflower risotto and finally the sautéed mushrooms.