Preheat oven to 425°F (220°C). Toss cauliflower florets with 1 tablespoon olive oil and a pinch of salt on a rimmed baking sheet. Cut the tops off the garlic bulbs, drizzle with a little oil, wrap in foil and place on the same sheet.

Roast cauliflower and garlic for 25–30 minutes, turning cauliflower once, until edges are browned and garlic is soft. Remove and let cool slightly; squeeze roasted garlic cloves from skins and set aside.

In a large heavy pot over medium heat, melt butter. Add chopped onion, diced carrot and celery and cook, stirring occasionally, until softened and starting to brown, about 6–8 minutes.

Stir in the flour and cook 1–2 minutes to make a light roux, stirring constantly so it doesn’t darken.

Slowly whisk in the vegetable broth to avoid lumps, then add the roasted cauliflower, squeezed roasted garlic, and bay leaf. Bring to a gentle simmer and cook 10 minutes to blend flavors.

Remove the bay leaf. Use an immersion blender to puree the soup until smooth (or carefully transfer in batches to a blender and puree, then return to the pot).

Stir in the milk and cream and warm gently over low heat—do not boil. Gradually add the grated cheddar, stirring until fully melted and smooth. If the soup is too thick, thin with a splash more broth or milk to reach desired consistency.

Season with salt, black pepper and smoked paprika to taste. Stir in lemon juice to brighten the flavor. Ladle into bowls and garnish with chopped chives and an extra sprinkle of cheddar if desired.