Place sausage in a skillet over medium-high heat, and cook until evenly brown. Drain, and set aside.
Preheat oven to 375 degrees F. Lightly grease a 9×13 inch baking dish. (I used a large springform pan lined with foil this time, just for fun!)
In a large bowl, beat together the eggs, condensed cream of mushroom soup, green chiles, cumin and milk. Place the frozen hash browns and sausage in the baking pan. sprinkle with half the cheese. Pour egg mixture on top and lightly stir ingredients to combine.
Bake in preheated oven for 50 to 60 minutes, or until set. Sprinkle with remaining cheese, and bake an additional 5 minutes, or until cheese is melted. Top with salsa, if desired!