In a large pot over medium heat, heat oil. Add onion and cook, stirring occasionally, until softened, about 7 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more. Add cauliflower and potatoes, stock, thyme, and bay leaf and bring to a simmer. Cook, stirring occasionally, until cauliflower is very tender, 15 to 20 minutes.
Remove thyme and bay leaf and discard. Blend with an immersion blender or transfer to a standard blender in batches and blend until smooth. Stir in cream and reheat if needed.
Divide soup among bowls. Drizzle with oil and top with thyme.
