Preheat your oven to 400°F (200°C). Spread the chunks of butternut and kabocha squash on a baking sheet, drizzle with olive oil, and toss to coat evenly. Roast for about 25-30 minutes until tender and lightly caramelized around the edges.
While the squash roasts, heat a tablespoon of olive oil in a large pot over medium heat. Add the chopped onion and sauté for about 5 minutes until translucent and fragrant, with a slightly golden hue.
Add the minced garlic to the onions and cook for another minute, stirring continuously until the garlic is fragrant. Be careful not to burn it.
Once the squash is roasted and cool enough to handle, carefully scoop the flesh into the pot with the sautéed onion and garlic.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Add cinnamon and nutmeg, then season with salt and pepper to taste. Let it simmer for about 10 minutes to let flavors meld.
Blend the soup directly in the pot using an immersion blender until smooth and velvety, or carefully transfer chunks to a blender and purée until creamy.
Taste and adjust seasoning with additional salt, pepper, or spices if needed. If the soup feels too thick, stir in a splash of warm water or broth and reheat gently.
Serve the soup hot, garnished with a drizzle of olive oil or a sprinkle of fresh herbs if desired. The smooth, slightly sweet aroma will invite you to enjoy each spoonful.