How to Make It
In a large saucepan, heat the olive oil. Add the onion and cook over moderately high heat, stirring occasionally, until golden, about 8 minutes. Add the apple cider and cook until syrupy, about 3 minutes. Add the butternut squash and chicken stock and bring to a boil. Cover and simmer until the squash is very tender, about 40 minutes.
In a blender, puree the soup in batches. Return the soup to the saucepan and stir in the cream. Season with salt and pepper and keep warm.
Heat a medium skillet. Add the butter and diced apple and cook over high heat until the apple is tender and golden around the edges, about 2 minutes. Remove the skillet from the heat. Season lightly with salt and pepper.
Ladle the soup into warmed bowls; garnish with the smoked cheddar, sautéed apples and chives; serve.