In a large skillet over medium-high heat, fry hash browns in butter and oil, and thinly slice the white part of a bunch of green onions. Season with salt and pepper and fry until golden brown.
Near the half way mark of reaching golden brown hash browns, add chopped deli beef and cheddar.
Once the mixture is sticking together and golden brown, remove from heat all to cool.
Spray muffin tin to grease. Spoon approximately 1-2 tablespoons into the muffin tins and press with fingers to the sides of the muffin tin forming a cup.
Drop an egg into each edible cup.
Season with salt and pepper.
Place in a 350 F (180 C) oven and bake 12-15 minutes depending on egg preference.