In a large stock pot, heat the oil over medium-high. Add onions, 1/3 cup cilantro, and garlic. Sauté 3 minutes.: You will first notice a gentle shimmer in the surface of the olive oil and a faint aroma as it warms. This is the cue to add your aromatics, because the hot oil is what extracts and carries their flavors into the soup. When you add the onion , cilantro , and garlic , pay attention to the sound, which should be a soft, steady sizzle rather than an aggressive spit. As the pieces contact the oil they will begin to soften and release sweet, savory scents; after about one to two minutes the raw edge of the onion will start to vanish and the garlic will sweeten. If you hear loud popping or see dark bits forming, lower the heat, because burnt aromatics will make the broth bitter. A common mistake is rushing the step with too high heat, which sacrifices that mellowed base flavor you want.
Stir in chicken broth, tomatoes, whole raw chicken breasts, all the spices, and 3/4 teaspoon salt. Push the chicken breasts to the bottom of the pot. Bring to a boil.: As you pour in the warm chicken broth and the diced fire roasted tomatoes , the pot will fill with a deeper, savory steam that balances acidity and umami. Nestle the two whole chicken breasts into the liquid so they are submerged; this ensures even cooking and allows the meat to infuse the broth with collagen and flavor. Sprinkle in the ground cumin , chili powder , cayenne pepper , and the bay leaves so their oils can bloom in the hot liquid. You will notice the surface begin to ripple as the pot approaches a boil; that is the time to leave it undisturbed for a moment so flavors meld. Avoid overboiling, because a furious boil can toughen the chicken and make the broth cloudy, which is a common pitfall here.
Add the carrots. Return to a boil, then reduce the heat to medium and cook another 10-12 minutes.: When the liquid returns to a boil, slipping in the thinly sliced carrots introduces mild sweetness and texture. Watch how the broth softens its surface and the aroma sweetens as the root vegetable releases sugars. Let the pot reach a gentle boil again and then reduce to medium so the cooking is steady and even. The carrots should become tender but still hold shape, which takes attention to timing. A frequent error is leaving them too long, which makes them limp and overly soft, losing the pleasant bite that contrasts the tender chicken .
Remove the cooked chicken breasts with tongs and either shred or chop them. Add the chicken pieces back to the soup.: During this interval the pot will sing softly with small bubbles and release fragrant steam; the chicken will firm and then relax as it cooks through. These minutes are when the flavors truly marry, as spices continue to infuse and the tomatoes release more body. Use this time to taste the broth and adjust if it needs salt, keeping in mind that you will add cheese and tortilla chips later which contribute saltiness. One mistake to avoid is guessing doneness by appearance alone; always check the thickest part of a chicken breast to ensure it is fully cooked.
Stir in half the cheese and 1 cup crushed tortilla chips. If too much of the broth has evaporated, stir in an additional cup of broth or water.: When the chicken is cooked, the meat will feel springy and release clear juices when pierced. Using tongs to transfer the breasts to a cutting board keeps things tidy and prevents overcooking. Shredding creates ribbons that soak up the broth and spices, while chopping yields bite sized pieces that disperse differently through each spoonful. Whatever method you choose, return the pieces to the pot so the meat can finish absorbing the flavors. A common slip is shredding while the meat is too hot to handle safely, so let it rest for a moment before working with it.
Ladle into bowls and top with the remaining cheese, fresh cilantro, fresh avocado, and more tortilla chip pieces.: As you fold in the shredded Monterey jack cheese and the crushed tortilla chips , notice the soup thicken subtly and the texture gain a slightly creamy body. The cheese melds into the warm broth, tempering spice and adding silkiness, while the chips act as a binder, giving the liquid a fuller mouthfeel. If the broth seems thinner than you expect, add an extra cup of chicken broth or water to reach your desired consistency. Avoid over stirring which can break down the chips too much and make the texture pasty rather than pleasantly thickened.
Ladle into bowls and top with the remaining cheese, fresh cilantro, fresh avocado, and more tortilla chip pieces: The final presentation is where the dish comes alive in both color and texture. Ladling the soup will release fragrant steam and the bowl will show off flecks of melted cheese and bits of shredded chicken . Scatter the remaining shredded cheese , fresh chopped cilantro , diced avocado , and crunchy tortilla chips for contrast and freshness. The cool avocado balances the warm spice and the crunchy chips add a pleasing snap. One thing to watch for is adding delicate garnishes too early, which makes them lose vibrancy, so always finish at the table.