Pat the chicken dry and season with salt and pepper. Heat 1 tablespoon of oil in a 10-inch, oven-safe pan over medium-high heat. When the oil is hot, add the chicken and cook on both sides until golden brown, 5-7 minutes total. Transfer to a plate and set aside.
Add the remaining oil, shallot, garlic, chipotle pepper and ¼ teaspoon of salt. Cook until fragrant, about 30 seconds, then add the broth and scrape up any browned bits. Bring the mixture to a simmer.
Stir in half the tortilla chips, then nestle the chicken into the broth and reduce heat to medium-low. Cook for 10-15 minutes, or until the chicken is cooked through. Transfer the chicken to a cutting board and shred or chop into bite-size pieces.
Return the shredded chicken to the skillet, along with the tomato, ½ cup of cheese and 1 tablespoon of cilantro. Stir in the remaining tortilla chips until they are incorporated and moistened.
Heat a broiler and place the broiler pan about 6 inches away from the heat. Sprinkle the remaining cheese on top of the casserole and broil until the cheese is melted and beginning to brown, 2-3 minutes. Top with remaining cilantro and allow to sit for 5 minutes before serving.