Core the cauliflower heads and cut the stems and florets into 1-inch pieces.
Bring 1 inch water to a boil in a large saucepan fitted with a steamer insert. Put the cauliflower into the pot, cover and steam until tender, 10 to 12 minutes. Lift the cauliflower pieces from the saucepan and spread out on a large platter lined with a clean kitchen towel. Let the cauliflower dry for 5 minutes.
Meanwhile, combine the oil, thyme and garlic in a small nonstick skillet. Cook over medium-low heat, stirring occasionally, until the garlic is fragrant and beginning to brown, about 3 minutes. Scrape the garlic oil into the bowl of a food processor.
Add the cauliflower, yogurt, Parmesan, and 1 teaspoon salt and several turns of black pepper to the food processor and blend until smooth and light, scraping down the bowl as needed. Transfer to a bowl and top with the butter and some more black pepper. Stir the butter into the cauliflower before serving.
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