Hearty and satisfying, this soup pairs perfectly with a crusty loaf of whole-wheat bread. This soup can be made up to two days ahead; for a thicker consistency, purée all or part of the soup.
Melt the butter in a large nonstick saucepan over low heat. Add the onion and increase the heat to medium-low. Cover and cook until tender, about 7 minutes. Stir occasionally.
Stir in the broccoli and the potato soup. Gradually stir in the milk until blended. Increase the heat to medium-high and bring to a boil. Reduce the heat to low and simmer, covered, until the broccoli is tender, about 5 minutes. Stir occasionally. Remove from heat; stir in the cheese until it melts. Add the mustard and cayenne, and stir to combine. Season to taste with salt and nutmeg, if desired.