Make the filling: in a medium bowl, combine chopped fresh spinach (or thawed, squeezed dry frozen spinach), cream cheese, Parmesan, mozzarella, minced garlic, 1/4 teaspoon black pepper, and salt to taste; mix until smooth and well combined.
Butterfly the chicken: place each chicken breast flat on a cutting board, place your hand on top, and slice horizontally about three-quarters of the way through to create a pocket, being careful not to cut all the way through.
Season the outside of each breast with chili powder, Italian seasoning, 1/2 teaspoon salt, and 1/2 teaspoon black pepper.
Stuff the chicken: spoon about one-quarter of the spinach-cream cheese mixture into the pocket of each chicken breast and fold closed; secure with toothpicks if needed to keep the filling inside.
Cook the chicken: heat 1 tablespoon olive oil in a nonstick skillet over medium-high heat. Add the stuffed breasts and cover with a lid. Cook 9–10 minutes per side, or until the internal temperature reaches 165°F and the chicken is cooked through.
Rest and serve: remove toothpicks, let the chicken rest 2–3 minutes, then serve.