Pre-heat the oven to 400. Line a baking sheet with parchment paper and set aside.
Bring a small, dry skillet over medium heat and add the pine nuts. Cook for 1-2 minutes, stirring occasionally until nuts are golden brown.
Transfer the toasted pine nuts, fresh basil leaves, 4 teaspoons of the Parmesan cheese, oil, water, lemon juice, garlic clove, nutmeg, salt and pepper to the bowl of your food processor and process until minced together into a pesto paste.
Place the chicken breasts on a cutting board. Using a meat mallet, pound the breasts to a ¼ inch thickness. Spread the pesto evenly across the surface of each breast. Sprinkle the sundried tomatoes and shredded cheese over the pesto. Starting with a short side, roll each breast up and seal the edges shut using a few toothpicks.
Place the rolled and sealed breasts in a Ziploc bag and add the flour (you may want to split this into two batches). Lightly flip the bag around until chicken is coated. Place the beaten egg white in a shallow dish. In a second shallow dish, mix the bread crumbs and Parmesan cheese. Remove each rolled breast from the flour bag and dip it in the egg white, turning to coat. Then move the coated breast to the breadcrumb dish and coat it with crumbs on all sides. Place the completed rolls seam side down on the prepared baking sheet.
Bake for 30-35 minutes. Don’t forget to remove the toothpicks before serving!