Melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook, stirring constantly, for 1 minute. Whisk in the milk, little by little, until thoroughly combined. Add the chicken stock and bring sauce to a boil. Reduce heat to a simmer and cook until thickened and flavorful, about 10 minutes. Add the pepper jack and stir until melted. Season with the salt and remove from the heat. Set aside, covered, while you assemble the remaining ingredients.
Heat a small skillet over high heat. When hot, add 1/2 teaspoon of the vegetable oil and 1 of the tortillas. Cook until soft, turning midway, about 1 minute per tortilla. Transfer to a plate and cover while you cook the remaining tortillas, adding additional 1/2 teaspoon of oil for each tortilla. Set aside on a plate and cover with plastic wrap or foil.
Preheat the oven to 350 degrees F. Lightly grease a 9-by 13-inch casserole.
Spoon 1 cup of the sauce onto the bottom of the casserole dish. Top with 6 of the tortillas, spreading them evenly to form a complete layer. Top with half of the chicken, 1 teaspoon of the Southwest Essence, half of the poblanos, half of the green onions, 1 1/2 cups of the sauce, and 1/3 of the shredded Monterey Jack. Make another layer in exactly the same way: 6 tortillas, the remaining chicken, 1 teaspoon of the Southwest Essence, remaining poblanos, remaining green onions, 1 1/2 cups of the sauce, and 1/3 of the shredded Monterey Jack. Top with the remaining 6 tortillas, remaining sauce, tomatoes, cilantro, and remaining Monterey Jack, then sprinkle the Queso Anejo evenly over the top.
Cover the casserole with aluminum foil and bake for 45 minutes. Remove the foil and continue to bake for about 15 minutes longer, or until the casserole is bubbly and light golden brown on top.
Serve immediately, garnished with a dollop of sour cream, more chopped cilantro, and a spoonful of salsa or pico de gallo, if desired.