Preheat your oven to 400°F (200°C).
On a baking sheet, toss the cauliflower florets with olive oil, salt, and pepper. Roast the cauliflower in the oven for about 25 minutes or until tender and slightly golden, turning halfway through.
While the cauliflower is roasting, heat a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5-7 minutes.
Add the roasted garlic cloves and sauté for another 2 minutes until fragrant.
Once the cauliflower is done roasting, add it to the pot with the sautéed onions and garlic mixture.
Pour in the broth and bring to a simmer. Cook for about 10 minutes to allow the flavors to meld.
Use a blender or immersion blender to puree the soup until smooth. If using a standard blender, allow the soup to cool slightly before blending in batches.
Return the blended soup to the pot, and stir in the shredded cheddar cheese until melted. Adjust seasoning with salt, pepper, and paprika to taste.
Ladle the soup into bowls and garnish with fresh chives or parsley, if desired. Serve hot.