Preheat the oven to 425°F and place a rack in the center. Use an oven-safe skillet or baking dish.
Slice the 2 poblano peppers and chop or slice the yellow onion per your preference.
Prepare the chicken breasts: for each of the 4 breasts, slice horizontally through the middle to within 1/2 inch of the other side to form a pocket.
Divide the 2 ounces cream cheese among the 4 breasts and spread it on one side inside each pocket. Put one slice of pepper jack cheese inside each breast (4 slices total). Divide the sliced poblanos and place some inside each breast. Close each breast and press to seal.
In a small bowl, combine 1 teaspoon chili powder, 1 teaspoon smoked paprika, 1 teaspoon garlic powder, kosher salt, and black pepper. Rub this seasoning mixture evenly over all sides of the stuffed chicken breasts.
Place the seasoned, stuffed chicken breasts in the skillet or baking dish. Scatter the remaining sliced poblanos and the chopped/sliced onion around the chicken.
Drizzle the 2 tablespoons extra virgin olive oil evenly over the chicken and vegetables. Pour the jar of salsa verde over and around the chicken.
Bake in the preheated oven 20–25 minutes, or until the chicken reaches 165°F and is cooked through.
Remove from the oven and let the chicken rest a few minutes. Serve with fresh cilantro and lime wedges.