1. To make the soup: In a large pot, heat olive oil over medium-high heat and sauté onion and apple until soft, about 10 to 15 minutes. Add garlic, salt, and cayenne, and let cook 1 minute more until fragrant.
2. Add broth and pumpkin, and bring to a boil. Remove from heat, and in batches, transfer soup to a blender and puree until smooth. Return to the pot, stir in the coconut milk and brown sugar, reheat, and season to taste.
3. For the Brussels sprout leaves: Preheat the oven to 375°F. Spread Brussels sprout leaves on a large rimmed baking sheet and toss with olive oil. Season with salt and pepper.
4. Bake for about 10 to 12 minutes until lightly browned and crisp.
To serve, divide soup into bowls and top with a spoonful of Crispy Brussels Sprout Leaves.