Slice the chicken through the middle horizontally to within a 1/2 inch of the other side.
Open the 2 sides and spread them out like an open book. Season the chicken on the inside and outside with a spice blend of salt, pepper, chili powder, garlic powder, and smoked paprika. Spread the cream cheese in the middle of the butterflied chicken, then add the pepper jack and poblano pepper slices. Close the chicken back up, like a book, which will enclose the filling. Repeat with all chicken breasts.
In oven safe heat 2 tbsp of olive oil over medium heat and then sauté poblano peppers and onions, for about 10 minutes, until softened but not browned.
Remove the skillet from heat, arrange stuffed chicken breasts over the sautéed onions and peppers, and then pour over the salsa verde. Bake 20–25 minutes, until the chicken is cooked through.