Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Wash and cut the cauliflower into florets, then toss them in a bowl with 1-2 tablespoons of olive oil, ensuring they're well coated. Season with salt and pepper.

Slice off the top of a whole head of garlic, drizzle it with olive oil, and wrap it in foil. Place the garlic and seasoned cauliflower florets on the prepared baking sheet. Roast together for 30-35 minutes, flipping halfway until golden brown and tender.

In a large pot, heat 1 tablespoon of olive oil over medium heat. Add the diced onion, sautéing for about 5-8 minutes until translucent and fragrant.

Squeeze the softened garlic out of its skin into a blender. Add the roasted cauliflower, sautéed onions, vegetable broth, and additional salt and pepper to taste. Blend until smooth and creamy.

Return the blended mixture to the pot over low heat, simmer and stir in the shredded sharp cheddar cheese until melted.

Taste and adjust seasoning if necessary. Serve the soup in bowls, garnished with sliced green onions and extra cheddar, alongside croutons or toasted sourdough.