Preheat the oven to 425°F (220°C).
Using a sharp knife, carefully slice each chicken breast horizontally without cutting all the way through, creating a pocket.
Spread softened cream cheese inside each chicken breast.
Add one slice of pepper jack cheese and a few poblano pepper slices to each pocket.
Fold the chicken closed and place it in a large oven-safe skillet or baking dish.
Brush the chicken with olive oil.
In a small bowl, combine the chili powder, smoked paprika, garlic powder, salt, and black pepper.
Rub the seasoning mixture evenly over each chicken breast.
Scatter the remaining poblano pepper slices and onion around the chicken.
Drizzle a little more olive oil over the vegetables.
Pour the salsa verde evenly around and over the One Skillet Cheesy Green Chile Chicken.
Bake for 20–25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove from the oven and let the chicken rest for 5 minutes.
Garnish with fresh cilantro and serve with lime wedges.