Preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper.
Toss cauliflower florets and chopped parsnips with 2 tablespoons olive oil, salt, and pepper. Spread them evenly on the baking sheet, adding the whole garlic cloves.
Roast for 25-30 minutes, stirring halfway through, until vegetables are golden brown and tender.
Meanwhile, heat remaining oil in a large pot over medium heat. Add diced onion and cook until translucent, about 5 minutes.
Add roasted vegetables, garlic, and thyme to the pot. Pour in the broth and bring to a simmer.
Cook for 10-15 minutes to let the flavors meld together.
Using an immersion blender (or working in batches with a regular blender), puree the soup until smooth.
Stir in the cream and adjust seasoning to taste.
Serve hot, garnished with fresh chives.