In a large skillet, cook sausage until done. In a large mixing bowl, beat eggs. Add sausage, sour cream, and chilies, whisking until combined.
Pour egg mixture over muffins. Press down lightly with the back of a spoon to moisten muffins. Sprinkle with cheese.
Bake, uncovered, for 35 to 40 minutes. Allow dish to stand for 10 minutes before serving.