In a saucepan, soften the shallot and garlic in the butter. Add the ham and cook for 2 minutes. Sprinkle with the flour and nutmeg and cook for 1 minute, stirring constantly.
Add the broth, cream and mustard. Bring to a boil over medium heat, stirring with a whisk. Simmer gently for about 5 minutes. Remove from the heat and stir in the cheese until completely melted. Add the broccoli and heat through, without boiling. Lightly season with salt and pepper.