Season the boneless skinless chicken breasts with kosher salt, black pepper, chili powder, smoked paprika, and garlic powder on both sides. Allow to sit for about 10 minutes.
In a large skillet, heat the extra virgin olive oil over medium-high heat. Once shimmering, add the chopped yellow onion and sliced poblano peppers. Sauté for 5-7 minutes until onions are translucent and peppers are tender. Remove and set aside.
In the same skillet, add the seasoned chicken breasts. Cook for 6-7 minutes on each side, or until the internal temperature reaches 165°F. Remove and set aside.
Lower the heat to medium, add the cream cheese, and stir until melted and combined with residual juices. Add salsa verde and simmer for 2-3 minutes.
Return chicken to skillet, spooning sauce over the top. Place a slice of pepper jack cheese on each breast, cover, and cook for an additional 2-3 minutes until cheese is melted.
Remove from heat, garnish with fresh cilantro, and serve with lime wedges. Enjoy!