Add olive oil to a large stock pot or Dutch oven over medium-high heat. Add the onions and cook for 4-6 minutes, stirring often. Add the poblano pepper, jalapeño, red, and green bell pepper. Cook for 5 minutes, stirring occasionally. Add the garlic and sauté for 1 minute.
Add the salt, cumin, ancho chili powder, ground coriander, Italian seasoning, canned tomatoes, and chicken broth (or water), to the pot. Cover soup and bring to boil over high heat. Reduce heat to a simmer over medium-low heat. Add the chicken breasts and return the lid to the pot.
Allow the chicken to cook for 25-30 minutes. Carefully remove the chicken breasts from the pot and transfer to a clean cutting board. Let rest until cool enough to handle then shred with a fork.
Return the shredded chicken back to the pot. Add the enchilada sauce, black beans, corn kernels, cilantro, green onion, and lime juice. Simmer for an additional 10-15 minutes.
Garnish with fresh cilantro, chopped green onion, lime juice, avocado, sour cream, and tortilla strips, if desired.