In a large saucepan, combine the broccoli with 3 cups of milk, mustard powder, salt, and pepper. Cover and bring to a simmer over medium-high heat. Decrease the heat to maintain a gentle simmer, and cook until the broccoli is tender, 10 to 15 minutes.
Slowly add the broccoli-milk mixture into the sauce, stirring to combine. Keep the soup chunky, or purée half of it in a blender until smooth, and then stir it back into the pot. Taste and adjust the seasoning.
Return the soup to a simmer over medium heat, and serve hot.