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Preheat oven to 450 degrees
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Heat 2 teaspoons of the olive oil over medium heat in a large Dutch oven or soup pot. Add the onion and sauté for a few minutes until slightly tender. Add the garlic and sauté another minute. Pour in the chicken broth and tomatoes and stir. Add the chicken breasts, being sure they are completely immersed in liquid. If not, add a little more broth until they are. Turn the heat to high. when the broth boils, reduce the heat so the liquid simmers. Set the timer for 10 minutes.
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While the soup is cooking, stack the tortillas on a cutting board and cut into 1/4-inch-thick strips. Drizzle the remaining 2 teaspoons of olive oil on a baking sheet, put the tortillas strips on the oil and use your hands to lightly coat the tortillas. Spread them out and sprinkle with a pinch of salt. Bake in the oven until lightly browned, about 5 minutes. Remove and set aside.
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After the chicken simmers for 10 minutes, add the carrots and cabbage to the broth, and continue to simmer until the carrots are tender and the chicken is cooked through (another 15 minutes or so). You can check this by cutting into the center of the chicken with a paring knife to have a peek.
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Remove the chicken from the broth and set aside until cool enough to handle. Turn off the heat.
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While the chicken cools, season the broth with the lime juice, cilantro and jalapeno (1/2 to 1 tablespoon depending on your personal tolerance for heat). Taste and add salt as needed, keeping in mind that the soup will be topped with cotija, which is quite salty. The chicken broth you use will play a big part in how much salt is required.
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Once the chicken is cool, pull the meat off the bones and shred into bite-size pieces. Add it to the soup and give it all a big stir.
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To serve, ladle the soup into bowls, sprinkle with the cotija followed by the tortilla strips and cubed avocado.