Cook the garlic in the oil in a large pot over medium heat, stirring, until golden, 2 to 3 minutes; remove and set aside the garlic. To the pot, add the cauliflower, chicken broth, thyme, 1 teaspoon salt, and ¼ teaspoon pepper. Simmer until tender, 15 to 20 minutes. Transfer the mixture to a blender and puree until smooth.
Top with the garlic, a drizzle of olive oil, and additional thyme before serving.