Melt the butter in a 5-qt stock pot. Add the onions and diced broccoli stems and sauté for 3 minutes. Add the ground mustard, salt and freshly ground black pepper. Sauté until the onion and broccoli stems start to soften – 4 more minutes. Stir in the flour and cook for 1 minute. Pour in the stock and half and half and bring the mixture to a boil, stirring as it thickens. Lower the heat, add a pinch of nutmeg and the broccoli florets, and continue to simmer with the lid askew for 15 minutes until the broccoli has softened.