In a large pot, heat 2 tablespoons of olive oil over medium heat. Add one large chopped onion and three minced garlic cloves; sauté for about 5 minutes until the onion is translucent and fragrant.

Stir in two seeded and chopped poblano peppers along with one seeded and chopped jalapeño pepper. Cook for an additional 5 minutes.

Sprinkle in one teaspoon of ground cumin, one teaspoon of smoked paprika, and half a teaspoon of chili powder. Toast the spices for about 1 minute.

Pour in four cups of chicken broth, stirring to combine the mixture. Raise the heat and bring to a gentle simmer.

Add two cups of shredded cooked chicken, one can of undrained diced tomatoes, and one can of drained black beans. Season with salt and pepper to taste.

Preheat the oven to 375°F (190°C). Spread six cut tortilla strips on a baking sheet, drizzle with olive oil, and bake for about 10 minutes.

Stir in the juice of one fresh lime and ¼ cup of chopped cilantro. Adjust the seasoning if necessary.

Ladle the hot soup into bowls, and garnish with diced avocado, shredded Monterey Jack cheese, crispy tortilla strips, and a dollop of sour cream if desired.