Preheat Oven to 400 degrees Fahrenheit. Combine Hash Browns, one egg, and melted butter. (When doubling this recipe, one egg is still sufficient.) Mix well. Grease two ramekins (about 4-5 inches in diameter) and press hash brown mixture into the bottom and around the sides to form a crust. Bake for 20-25 minutes until the the edges are lightly browned.
Meanwhile, stir together condensed soup, milk, green onions, basil and mustard. Mix well. In a separate bowl combine chopped meat, bread crumbs and melted butter. Toss to mix.
When the crusts are browned, crack two eggs into each ramekin. Spoon the soup mixture evenly around the yolks in the ramekin (there will be some (maybe a lot) left over. Sprinkle the meat mixture evenly over the dishes. REturn to oven and bake 25 minutes for solid yolks, 20 minutes for softer yolks, your oven may vary. Let stand 5 minutes before serving. It will be hot!