Heat the butter in a saucepan until melted and butter stops foaming. Stir in the flour to make a roux. Cook over medium-low heat until smooth, stirring constantly; remove from heat.
Whisk the eggs in a bowl until blended. Add baking powder, white pepper and milk; whisk until combined.
Slowly add the roux, stirring constantly. Remove from heat and add cream cheese. Stir in the Monterey Jack cheese, cottage cheese and green chile.
Pour the mixture into a greased 9×13-inch baking pan. Bake at 350 degrees for 45 minutes or until set. (If using individual quiche dishes, bake for about 35 minutes. Be sure to spray dishes well to keep them from sticking.)