Preheat the oven to 400°F (200°C) and lightly grease a medium-to-large baking dish with a little olive oil.
Heat 1 tablespoon olive oil in a skillet over medium heat. Add the fresh spinach and cook for 2–3 minutes until wilted. Add the minced garlic and cook for another 30–45 seconds until fragrant. Remove from the heat and drain any excess moisture from the spinach.
Add the cooked spinach and garlic to a mixing bowl along with the chopped roasted red peppers, 1 cup shredded mozzarella, softened cream cheese, Parmesan, 1 teaspoon Italian seasoning, parsley, lemon juice, ½ teaspoon salt, and ¼ teaspoon black pepper. Mix until evenly combined.
Place each chicken breast on a cutting board and carefully cut horizontally through the thickest part, stopping before cutting completely through. Open each breast like a book to create a pocket.
Combine the remaining ½ teaspoon salt, ¼ teaspoon black pepper, smoked paprika, garlic powder, and remaining ½ teaspoon Italian seasoning. Brush the chicken with the remaining 1 tablespoon olive oil and season both sides and the inside of each breast.
Divide the filling evenly among the four chicken breasts, placing it inside the pocket while leaving about ½ inch around the edges. Do not overfill.
Fold each chicken breast closed over the filling and secure the opening with one or two wooden toothpicks. Place the stuffed chicken breasts in the prepared baking dish in a single layer.
Bake for approximately 25–32 minutes, depending on the thickness of the chicken, until the thickest part reaches 165°F (74°C) when checked with an instant-read thermometer.
For a more golden top, broil the cooked chicken for 1–2 minutes, watching closely so the cheese and seasoning do not burn.
Remove the chicken from the oven and let it rest for 5 minutes. Carefully remove all toothpicks, then slice the chicken and garnish with additional fresh parsley or a squeeze of lemon if desired.