Preheat the oven to 400°F (200°C). Line 1 large baking sheet with parchment paper.
Place the squash cut side up on the baking sheet. Cut the garlic in half and place them in the holes of the squash. Add the rest of the vegetables: peppers, tomatoes, carrots, onion wedges.
Drizzle with olive oil and season with salt and pepper.
Roast everything for 50-60 minutes, stirring once halfway through, until the edges are caramelized and everything is tender.
Let cool slightly, then scoop out the squash flesh and squeeze roasted garlic cloves out of their skins.
Add all roasted vegetables to a large pot or blender, with smoked paprika and dry thyme.
Add 4 ½ cups of chicken or vegetable broth.
Blend until completely smooth.
Adjust thickness by adding more broth.
Return the soup to heat and bring to a gentle simmer for 10 minutes. Taste and adjust with extra salt and pepper.
Ladle into bowls, swirl in cream and garnish with chili flakes or herbs.
Serve with toasted sourdough or garlic croutons.