In a large saucepan, melt butter over medium heat. Add apples, carrots, onion, garlic, ginger, curry powder and mustard; cook, stirring occasionally for 5 to 7 minutes, or until onion begins to soften.
Add broth and apple cider; bring to a boil. Reduce heat and simmer. partially covered, for 15 to 20 minutes, or until vegetables are very tender.
In a food processor or blender, puree till smooth. Season with salt and cayenne pepper to taste.
Ladle into four bowls. Sprinke each serving with 1/4 cup Cheddar cheese.