Roast the garlic. Preheat oven to 400°F (200°C). Slice the top off the garlic bulb to expose the cloves. Drizzle with a little olive oil, wrap tightly in foil, and roast until the cloves are soft and golden, about 30–35 minutes. Let cool, then squeeze the softened cloves from their skins.

Sweat the onion. Warm the remaining olive oil in a large soup pot over medium heat. Add the chopped onion and cook, stirring occasionally, until it becomes translucent and fragrant — about 4–6 minutes.

Brown the cauliflower a bit. Add the cauliflower florets to the pot and cook for a few minutes, stirring, so they pick up a touch of color and deeper flavor.

Simmer. Pour in the broth and drop in the roasted garlic cloves. Bring the pot to a boil, then lower the heat and simmer until the cauliflower is tender, roughly 15–20 minutes.

Puree until smooth. Use an immersion blender to purée the soup directly in the pot until silky. If you prefer, blend in batches in a countertop blender — be careful with hot liquid.

Finish with dairy and cheese. Return the blended soup to low heat. Stir in the milk or cream, then add the grated cheddar a handful at a time, stirring until each addition melts completely. Don’t let the soup boil after adding the cheese.

Season and serve. Taste and adjust salt and pepper. Ladle into bowls and sprinkle with chopped chives or parsley. Serve with warm bread or crackers.