Preheat oven to 450°F. In a 1.5 quart dish, combine butter, sauce mix, boiling water, and milk. Whisk together until sauce mix dissolves. Add potatoes, ham, and broccoli, and stir.
Bake in preheated oven for 20 minutes. Remove from oven, top with shredded cheese. Return to oven for an additional 5 minutes, until cheese is melted. Let sit for 5 minutes before serving.