Preheat the oven to 425°F (220°C).
On a cutting board, slice each chicken breast horizontally almost through, leaving about 1/2 inch intact so it opens like a book.
Spread about 1/2 ounce cream cheese on one side of each opened breast, top with a slice of pepper jack and a few slices of poblano, then fold the chicken closed to enclose the filling.
Place the stuffed chicken breasts in an oven-safe skillet or baking dish and rub them with 1 tablespoon olive oil.
In a small bowl, mix the chili powder, smoked paprika, garlic powder, and a generous pinch of kosher salt and black pepper.
Rub the spice mixture all over the chicken breasts.
Scatter the remaining sliced poblano peppers and the chopped or sliced yellow onion around the chicken in the skillet. Drizzle with the remaining 1 tablespoon olive oil.
Pour the jar of salsa verde evenly over the chicken and vegetables.
Bake in the preheated oven for 20–25 minutes, until the chicken reaches an internal temperature of 165°F (74°C) and is cooked through.
Serve the chicken topped with fresh cilantro and lime wedges.