Layer 1/3 chilies and 1/3 cheese. Repeat this 2 times for a total of three layers.
Add flour and milk to eggs. Blend well. Pour mixture over chilies and cheese.
At this point the dish can be refrigerated up to 24 hours.
Bake 350 degrees for 60 minutes.
Top with Salsa Verde and remaining cheese, and bake for an additional 15 minutes.
Cool until warm and cut into squares.