Cut the cream cheese into ½-inch cubes and set out to soften. Dice the onion and bell pepper, mince the garlic, drain and rinse the beans, open the cans, mix the spices in a small bowl, shred the cheddar, and pat the chicken dry.
Heat the olive oil in a Dutch oven over medium heat. Sauté the onion and bell pepper for 5 to 6 minutes until translucent, then stir in the garlic for 30 seconds and the spice mixture for 30 seconds until fragrant.
Pour in the enchilada sauce and broth, scraping up browned bits. Add the tomatoes and green chiles with their liquid, stir in the beans and corn, and nestle the chicken breasts fully into the liquid. Bring to a boil.
Reduce the heat to medium-low, cover, and simmer for 20 to 25 minutes, stirring once or twice, until the chicken reaches 165°F (74°C) on an instant-read thermometer.
Lift the chicken out, shred it into bite-size strands with two forks or meat claws, and return it with any juices to the pot.
Reduce the heat to low until the soup stops bubbling. Stir in the softened cream cheese until melted, then add the cheddar a handful at a time, stirring until smooth. Taste and add salt as needed, then remove from the heat.
Ladle into 6 bowls and top each with tortilla strips, sour cream, diced avocado, cilantro, and a lime wedge squeezed over just before eating.