In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.

Add the minced garlic, bell pepper, and carrots; cook for another 3-4 minutes until the vegetables start to soften.

Stir in the ground cumin, chili powder, smoked paprika, and cayenne pepper (if using) until the spices are fragrant, about 1 minute.

Pour in the chicken broth, and add the black beans, diced tomatoes, shredded chicken, and corn. Season with salt and pepper to taste.

Bring the soup to a simmer and let it cook for about 20 minutes, allowing the flavors to meld together.

While the soup is simmering, heat a separate skillet over medium heat. Place a flour tortilla in the skillet and sprinkle with cheese. Top with another tortilla and cook until the bottom is golden brown, about 2-3 minutes.

Flip the quesadilla and cook for an additional 2-3 minutes until the cheese is melted and the other side is golden brown. Remove from the skillet and repeat with the remaining tortillas and cheese.

Cut the quesadillas into wedges and serve them alongside the soup. Top each bowl of soup with a dollop of sour cream, fresh cilantro, and lime wedges.