1. Melt butter in a stockpot over medium heat. Add onions and saute until tender, about 3-5 minutes.
2. Sprinkle the flour and mustard powder on top and stir to evenly coat; continue to stir for 1 minute.
3. Pour in chicken stock, stirring until well blended.
4. Peel, core and chop 3 granny smith apples and add to the soup. Cook until soup is thickened and apples soft, about 10 minutes.
5. Add the cheddar cheese and cook a few minutes longer, until the cheese is completely incorporated.
6. Use an immersion blender or regular blender to puree the soup until smooth.
7. If using, peel, core and chop the last apple and either stir into the soup or serve on the side as apple "croutons".
8. Add salt and pepper to taste and serve.
Makes 4 main dish or 8 appetizer servings.