Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
Add cauliflower florets to the sheet pan. Drizzle with 1–2 tablespoons olive oil, season generously with salt and pepper, and toss to coat evenly.
Prepare the garlic by removing the outer papery layers while keeping the cloves intact. Slice ¼ inch off the top to expose the cloves. Drizzle with olive oil, wrap loosely in foil, and place on the baking sheet with the cauliflower.
Roast for 30–35 minutes, flipping the cauliflower halfway through, until golden and caramelized.
While roasting, heat 1 tablespoon olive oil in a large pot over medium heat. Add diced onion and sauté for 5–8 minutes until soft and translucent.
Allow garlic to cool slightly, then squeeze roasted cloves from their skins.
In a high-speed blender, combine sautéed onion, roasted cauliflower, roasted garlic, vegetable broth, salt, and pepper. Blend until completely smooth.
Pour the mixture back into the pot and bring to a light simmer.
Stir in shredded cheddar cheese until melted and incorporated. Simmer for 10–15 minutes. Taste and adjust seasoning as needed.
Serve Roasted Garlic Cheddar Cauliflower Soup warm, garnished with green onion, extra cheddar, and toasted bread.