Preheat oven to 400 degrees. Grease muffin pan and set aside.
Combine hash browns, cheese and melted butter in a bowl. Season generously with salt and pepper. Divide evenly among 8 greased muffin wells. Press potato mixture along the bottom and up the sides of the wells to form “cups”. Bake for 20-25 minutes or to desired degree of doneness. You can lightly cover with foil if the edges are browning too quickly. Allow to cool slightly if using immediately (or cool completely if storing cups in refrigerator).
Divide sausage crumbles evenly among muffin wells. Crack one egg over sausage into each muffin well and bake for 8-12 minutes or to desired degree of doneness. Season with salt and pepper and sprinkle with chopped chives, if desired.
Note: This recipe is easily doubled for large groups.