Place large pot on stovetop over medium heat. Add 1 tablespoon neutral-flavored oil and continue heating pot until oil is hot and shimmery.
When oil is hot, add 1 cup diced white onion, ½ cup chopped carrots, and ½ cup chopped celery to pot. Stir to incorporate. Sauté vegetables, stirring often, approximately 10 minutes or until vegetables have softened and onions are translucent.
Once vegetables have softened, add 3 tablespoons minced fresh garlic to pot and stir to incorporate. Sauté ingredients, stirring occasionally, 30 to 60 seconds or until garlic is just fragrant.
When garlic is fragrant, pour 4 cups chicken stock into pot. Stir to incorporate stock, scraping bottom of pot with spoon or spatula to loosen any vegetables that may have stuck to pot.
Add 1 14.5-ounce can crushed tomatoes, 1 large jalapeño, 1 teaspoon cumin, 1 teaspoon ground coriander, and 1 teaspoon salt to pot. Stir to incorporate.
Increase heat under pot to high and bring liquid to boil.
Once liquid begins to boil, immediately reduce heat under pot to low. Simmer soup, uncovered, 15 minutes.
After 15 minutes, add 3 cups shredded cooked chicken to pot and stir to incorporate. Simmer soup approximately 5 minutes or until chicken is warmed through.
Add ¼ cup chopped fresh cilantro to pot and stir until cilantro is just incorporated.
Once cilantro is incorporated, ladle soup into serving bowls. Garnish with tortilla strips and lime wedges if desired. Serve immediately.