Preheat oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Toss the cauliflower florets with 2 tablespoons of olive oil, 1/2 teaspoon of salt, and 1/4 teaspoon of black pepper directly on the baking sheet until evenly coated.
Spread the florets in a single layer and roast for 25 to 30 minutes, tossing halfway through, until the edges are golden brown and caramelised.
Heat the remaining 1 tablespoon of olive oil in a large Dutch oven over medium heat.
Add the diced onion and sauté for 5 to 7 minutes until translucent and soft.
Add the minced garlic and cook for 1 minute until fragrant.
Reserve 1/2 cup of the prettiest roasted cauliflower florets for garnish; add the remaining cauliflower, vegetable broth, and dried thyme to the pot.
Bring the liquid to a boil, then reduce heat to low and simmer, partially covered, for 15 minutes to integrate flavors.
Remove the pot from heat and use an immersion blender to process the soup until completely smooth and velvety.
Stir in the heavy cream and ground nutmeg, then return to low heat for 2 minutes to warm through.
Adjust seasoning with additional salt and pepper as needed.
Ladle into bowls and garnish with the reserved roasted florets and chopped chives.