Spray a large 13 x 9 x 2-inch casserole dish with vegetable spray and set aside.
Heat the Olive Oil (1 tablespoon) in a large skillet over medium high heat and add the Bell Pepper (1) and Onion (1 cup). Sprinkle with Kosher Salt (1 pinch).
Saute the vegetables until softened, about 3 to 5 minutes. Add the Hatch Chili Pepper (1 1/2 cup) and continue to saute until most of the liquid has evaporated. Remove from heat.
In a large bowl, combine the Egg (8), Kosher Salt (1/2 teaspoon), and Freshly Ground Black Pepper (1/2 teaspoon). Whisk the eggs, then add the Milk (3 cup) and whisk to combine.
Layer the casserole: Add the Country White Bread (6 cup) to the casserole dish and spread into an even layer. Sprinkle with one cup of the Monterey Jack Cheese (1 cup) and 1 cup of the Sharp Cheddar Cheese (1 cup).
Sprinkle the peppers in an even layer over the cheeses.
Pour the egg mixture over the peppers and sprinkle on the remaining cup of Monterey Jack Cheese (1 cup) and half cup of Sharp Cheddar Cheese (1/2 cup). Lightly press the contents into the egg mixture. Cover with plastic wrap and refrigerate overnight.
Preheat the oven to 350 degrees F (180 degrees C).
Bake the strata uncovered for 45 to 55 minutes, or until bubbly and lightly browned.