Preheat the broiler on high.
Place the poblano peppers on a baking sheet and broil for 8-10 minutes, turning occasionally, until the skins are charred and blistered.
Transfer the peppers to a bowl and cover tightly with plastic wrap. Let them steam for 15 minutes.
Peel the skins off the peppers, remove the stems and seeds, and roughly chop the roasted peppers. Set aside.
Heat olive oil in a skillet over medium heat. Add diced onion and cook for 4-5 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant. Remove from heat.
Place the chicken breasts in the slow cooker. Add the cooked onion and garlic, chopped roasted poblano peppers, chicken broth, diced tomatoes with their juice, ground cumin, dried oregano, smoked paprika, cayenne pepper, salt, and black pepper.
Cover and cook on low for 6 hours, or until the chicken is cooked through and tender.
Remove the chicken breasts from the slow cooker and shred them with two forks.
Return the shredded chicken to the slow cooker. Stir in the frozen corn kernels and cook for an additional 15 minutes on low to heat through.
Ladle the soup into bowls. Top each serving with shredded Monterey Jack cheese and chopped fresh cilantro.
Serve with lime wedges on the side for squeezing over the soup.