Heat the olive oil in a large Dutch oven or pot over medium heat. Add the onion and bell pepper and cook until softened, about 5-7 minutes.
Add the garlic and jalapeño and cook for 1 minute, until fragrant.
Stir in the cumin, chili powder, smoked paprika, oregano, and cayenne pepper (if using). Cook for 1 minute.
Add the black beans, corn, diced tomatoes, green chiles, and chicken broth. Stir to combine.
Add the chicken breasts to the pot. Bring the soup to a boil, then reduce heat to low, cover, and simmer for 20-25 minutes, or until the chicken is cooked through.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the soup.
Stir in the heavy cream and cilantro. Season with salt and pepper to taste. Simmer for 5 more minutes.
Serve the soup topped with shredded cheese, avocado, sour cream, a squeeze of lime juice, and tortilla strips.