Preheat oven to 425°F (220°C).
Slice squash vertically down the center, scoop out the seeds, and place the halves cut-side down on a baking sheet lined with parchment paper. Rub 1 tablespoon of olive oil on the outside skin of the squash, and bake in the oven for about 30 minutes (or until almost tender).
Allow squash to cool, peel the skin off, and cut squash into 2-inch cubes. Set aside.
Next, in a large pot, heat remaining 1 tablespoon of olive oil over medium-high heat. Saute onions until slightly brown, about 3-4 minutes, adding a pinch of salt as they cook. Stir in garlic, ginger and cayenne pepper and cook for 1 more minute.
Add 2 cups of the stock, brown sugar (or maple syrup), and squash and bring to a boil. Cover, reduce heat, and simmer for about 10-15 minutes (or until the squash is very tender). Remove from heat.
Puree soup with an immersion blender or puree in batches in a regular blender or food processor, adding remaining stock slowly until the soup reaches the desired consistency.
Season with salt and pepper to taste and garnish with optional toppings.