Heat olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and garlic, cooking until softened and fragrant, about 3-4 minutes.
Stir in the red bell pepper, corn, and zucchini. Cook for another 5 minutes until the vegetables are slightly tender.
Add the diced tomatoes, shredded chicken, chicken broth, chili powder, cumin, smoked paprika, salt, and black pepper into the pot. Stir well to combine.
Bring the soup to a gentle boil, then reduce the heat and let it simmer for about 15 minutes, allowing the flavors to meld.
Stir in the enchilada sauce and heavy cream. Cook for an additional 5-10 minutes until heated through. Taste and adjust seasonings as needed.
Remove from heat and stir in half of the shredded cheese until melted and combined.
Serve the soup hot, garnished with fresh cilantro, a sprinkle of additional cheese, and lime wedges on the side.