Preheat an oven to 425 degrees F (220 degrees C). Line a baking sheet with aluminum foil. Coat the jalapeno and poblano peppers with 1 tablespoon olive oil and arrange on the prepared baking sheet.
Roast peppers in the oven until charred, 30 to 40 minutes, turning once about half way through the cooking time. Remove peppers from oven and set aside to cool.
Reduce oven heat to 350 degrees F (175 degrees C). Spray a 9x13-inch baking dish with cooking spray.
Heat the remaining 1 tablespoon olive oil in a skillet over medium heat. Stir in the celery, garlic and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Season with 1 teaspoon salt and black pepper to taste. While the onion mixture is cooking, remove the skin and seeds from the cooled peppers, then coarsely chop. Stir peppers into the skillet and cook for 1 to 2 minutes more. Stir in the cream of chicken, cream of celery, chicken broth, chili powder, cumin, and chicken meat.
Make a single layer using half of the strips of tortilla on the prepared baking dish. Spread half of the chicken mixture on top. Sprinkle with salt to taste, and top with half of the Monterey Jack cheese. Repeat the layers, finishing with the remaining half of the Monterey Jack cheese.
Bake in the preheated oven until the cheese is bubbly and the edges are golden brown, 25 to 35 minutes. Allow the dish to rest for 5 to 10 minutes before serving.
