Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Make the Filling: In a medium bowl, combine the Boursin cheese, spinach, sun-dried tomatoes, Parmesan, and basil. Set aside.
Prepare the Chicken Mixture: In a large bowl, combine the ground chicken, egg, Parmesan, garlic, Italian seasoning, salt, and black pepper. Mix gently until just combined.
Shape the Chicken: Divide the chicken mixture into 4 equal portions. Place the portions on the prepared baking sheet, leaving space between them. Using your hands, flatten each portion into a 6- to 7-inch oval about ¼-inch thick.
Fill and Fold: Spoon one-quarter of the filling down the center of each chicken oval, leaving about a ½-inch border around the edges. Using kitchen scissors, cut the parchment paper between the ovals. Lift one side of the parchment paper and use it to gently fold the chicken over the filling, making a half-moon shape. Carefully peel away the parchment. There's no need to seal the edges—the filling stays in place as the chicken bakes.
Add the Topping: In a small bowl, combine the Parmesan, panko breadcrumbs, and Italian seasoning. Lightly spray the tops of the chicken pockets with cooking spray. Sprinkle the topping evenly over each pocket, then lightly spray again.
Bake for 22 to 25 minutes, or until the chicken is cooked through and an instant-read thermometer inserted into the thickest part registers 165°F (74°C). For a deeper golden color, broil for 1 to 2 minutes at the end of cooking.
Let the chicken pockets rest for 5 minutes before serving. Garnish with additional basil, if desired.