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 cook for an additional minute until fragrant.
Add the diced poblano peppers and chicken to the pot. Cook until the chicken is no longer pink, about 5-7 minutes.
Pour in the chicken broth and bring the mixture to a boil. Reduce heat and let simmer for 15 minutes.
Stir in the heavy cream, corn, diced tomatoes, cumin, smoked paprika, salt, and pepper. Simmer for another 10 minutes, allowing the flavors to meld.
Remove from heat and stir in the chopped cilantro and lime juice. Adjust seasoning if necessary.
Serve hot, garnished with additional cilantro if desired.