Pre cook and shred chicken.

Adjust oven racks to top third and lower third positions and preheat oven to 400ºF (205ºC). Arrange tortillas on 2 large rimmed baking sheets (they will be slightly overlapping). Lightly spray both sides with cooking spray. (Alternatively, use pastry brush to lightly brush tortillas with a thin layer of neutral oil.)

Bake until slightly crisp and browned in spots, about 14 minutes, flipping tortillas halfway through and rotating baking sheets between top and bottom racks. Remove from oven and let cool until ready to use. (Tortillas will continue to crisp as they cool.)

In a large pot or Dutch oven set over medium-high, melt butter. Add onion, bell pepper, poblano, and garlic; cook, stirring occasionally, until softened, about 8 minutes. Add flour, chili powder, and granulated chicken bouillon. Cook, stirring often, until fragrant and flour just begins to stick to bottom of the pot, about 1 minute. Add diced tomatoes and green chiles, cream, and 2 ½ cups broth; bring to a simmer over medium-high. Simmer, stirring occasionally, until slightly thickened, about 4 minutes. Remove from heat, and stir in cilantro, sour cream, salt, and shredded chicken until thoroughly combined.

To assemble, place 6 tortillas in the bottom of a 9- by 13-inch baking dish. Spoon 3 cups of the chicken mixture over tortillas, and top with ½ cup of Monterey Jack cheese. Repeat with second layer. Top with remaining 6 tortillas, remaining 2 cups chicken mixture, and remaining 1 ½ cups cheese.

Bake, uncovered, at 400°F on top third rack of oven until bubbling and browned, 15 to 20 minutes. Garnish with additional cilantro.