Preheat oven to 350°F Put each chicken breast half between two layers of plastic wrap, on a chopping board, and use a meat mallet to pound until 1/4-inch thick.
Dip each basil (or other bitter green) leaf in boiling water, drain and set aside.
If you are not starting with Boursin herbed cheese, make your own by mixing together the Herbed Cheese ingredients mentioned above. Mix the walnuts into the cheese mixture, set aside.
Lay the chicken breasts flat, season each side with salt and pepper. Spread the cheese-walnut mixture over each breast, covering the surface of the breasts. Layer on the basil leaves. Starting at the shortest end of the chicken breast, roll up as tightly as possible and tuck in the ends to form a neat roll. Secure each breast with 2 toothpicks.
Put flour, beaten egg, and bread crumbs combined with the Parmesan cheese on to 3 separate flat dishes. Dredge each chicken breast roll first in the flour, then the egg, and finally the Parmesan bread crumbs. (Skip this step if you are going low carb and/or gluten-free.).
Transfer chicken breasts to a greased baking dish, seam side down. Bake at 350°F for 40-50 minutes, depending on the size of the breast, until the internal temperature is 165°F, the juices run clear, and the chicken is slightly browned.
Let rest for 5 minutes before serving.