Preheat oven to 200°C (400°F). Spread the cubed squash on a large baking sheet in a single layer. Drizzle with 2 tablespoons olive oil, season with ½ teaspoon salt and black pepper, and toss to coat evenly.
Roast for 25 to 30 minutes, turning once halfway, until the edges are golden and a fork slides in without resistance.
Heat the remaining 1 tablespoon olive oil and the butter in a large pot over medium heat. Cook the onion for 7 to 8 minutes until soft and lightly golden at the edges.
Add the garlic and cook 1 minute. Add cumin, cinnamon, nutmeg, and ginger. Stir constantly for 30 to 45 seconds until the spices darken slightly and smell toasted.
Transfer the roasted squash into the pot. Pour in the vegetable stock and stir to combine. Bring to a gentle boil, reduce to a low simmer, and cook for 10 minutes.
Remove from heat. Blend with an immersion blender until completely smooth, 1 to 2 minutes. If using a countertop blender, fill it halfway at most, hold the lid with a folded kitchen towel, and start on low speed.
Return to medium-low heat. Stir in the heavy cream and optional brown sugar. Taste and adjust with salt, pepper, and a squeeze of lemon juice. Heat through for 2 to 3 minutes without boiling.
Ladle into bowls. Garnish with a swirl of cream, toasted pepitas, fresh thyme leaves, and a pinch of smoked paprika.