Place the oil, onions, and Poblano in a soup pot, and then sauté the mixture for five minutes while the heat is set to medium.
Mix in the garlic, jalapeño, cumin, and chili powder until they are well distributed. Cooking should be continued for another 5 minutes.
Utilizing a blender, combine the tortillas with the stock from the soup. Purée until it's almost completely smooth.
Toss the fire-roasted tomatoes and smashed tomatoes in once the tortillas and broth mixture has reached a boil.
Reduce the temperature, then stir in the spice mixture along with the shredded chicken. Cook for 15 minutes at a heat setting of medium-low.
As a garnish, add crumbled tortilla chips and Monterey Jack cheese and season it to taste with salt and pepper.