1. In a large stockpot, melt the butter in the vegetable oil. Add the onion and garlic and cook over high heat, stirring, until softened but not browned, about 4 minutes. Add the curry and cook, stirring, for 1 minute. Add the squash and cook, stirring, for 4 minutes. Add 6 cups of the stock and bring to a boil. Cover and simmer over moderately low heat until the squash is tender, about 30 minutes.
2. Meanwhile, arrange 4 of the Cheddar squares in a large nonstick skillet and cook undisturbed over moderate heat until bubbling, about 1 1/2 minutes. Sprinkle each square with a small pinch of the cumin seeds and 3 or 4 almond slices; cook until the edges are golden and the cheese is set, about 1 1/2 minutes longer. Using a thin spatula, flip the cheese crisps and cook until the almonds are lightly browned, about 20 seconds longer. Transfer to a baking sheet lined with paper towels and let cool until crisp. Wipe out the skillet and repeat with the remaining Cheddar, cumin seeds and almonds.
3. Working in batches, puree the soup in a blender. Return the soup to the pot and gradually stir in about 2 cups of stock, until the soup has a silky, bisquelike consistency. Season with salt and pepper and keep warm over low heat.
4. Ladle the soup into shallow bowls and pass the Cheddar crisps alongside for dipping or crumbling.
Make Ahead: The soup can be refrigerated for up to 3 days. The Cheddar crisps can be stored overnight in an airtight container. Recrisp on a baking sheet in a 350° oven and let cool.