Put first 7 ingredients into medium bowl. Beat on medium until mixed.
Add cheese and green chilies. Stir. Turn into grease 8x8-inch baking dish. Bake in 350F oven for 45 to 55 minutes until set and lightly browned on top.
Cuts into 25 pieces.
Bake ahead. Cool completely. Do not cut. Cover and chill for up to 24 hours or freeze for up to 6 months. Remove from refrigerator about 30 minutes before serving. Cut while still cold. Remove from freezer 1 to 2 hours before serving. Cut while still partially frozen.
As an alternative, reheat just before serving in 325F oven for 5 to 10 minutes. Serve warm.