In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and diced poblano peppers, cooking for an additional 2 minutes until fragrant.
Add the diced chicken to the pot and cook until no longer pink, about 5-7 minutes.
Pour in the chicken broth, heavy cream, ground cumin, and smoked paprika. Season with salt and pepper. Bring to a simmer.
Add the corn and diced tomatoes, stirring to combine. Let the soup simmer for 15-20 minutes, allowing the flavors to meld.
Stir in the chopped cilantro and lime juice just before serving. Adjust seasoning if necessary.
Serve hot, garnished with additional cilantro if desired.