Preheat the oven to 375°F.
Cover the bottom of a baking sheet with parchment paper or tin foil sprayed with cooking spray. In a small bowl, combine the salt and pepper. Sprinkle and pat this mixture onto both sides of the chicken.
On a large plate, place one chicken breast smooth side down, with the narrowest end closest to you. Place 1 tablespoon of pesto onto the center of the breast. Spread the pesto evenly over the breast using a pastry brush.
Sprinkle 2 tablespoons of shredded cheese over the pesto, keeping a ½ inch cheese-free border around the breast. Starting at the end closest to you, carefully roll up the chicken breast.
Using 4 toothpicks, secure the end of the breast. Place the breast, toothpick side down, on the prepared baking sheet. Repeat steps with the remaining chicken breasts.
Slowly pour 1 teaspoon of oil over each breast. Use a pastry brush to coat the top and the sides of each breast. Place 1½ teaspoons of Dijon mustard on top of each breast. Use a pastry brush to coat the top and sides of each breast.
Carefully sprinkle 1 tablespoon of bread crumbs over the top and along the sides of each breast, using your fingers to pat the crumbs onto the sides. Bake until the chicken is firm and no longer pink inside, approximately 20 to 25 minutes.
Remove the chicken from the oven and let stand for 5 minutes before removing the toothpicks. Using a chef’s knife, slice each breast ½-inch to 1-inch thick on the diagonal before serving. Serve and enjoy!