Heat oven to 425°F (220°C).
Spread broccoli, onion, and garlic on a baking tray.
Drizzle with olive oil. Add black pepper and a pinch of salt.
Roast for 25–30 minutes, flipping once, until edges are golden.
Add roasted vegetables to a large pot.
Pour in vegetable broth. Add potato and cauliflower.
Bring to a gentle boil, then lower heat.
Simmer for 12–15 minutes until everything is soft.
Blend until smooth using an immersion blender or blender.
Taste and adjust seasoning.
For cheese soup, turn off heat and stir in cheddar slowly.