Place the 4 whole eggs in a pot and cover with water. Bring to a boil and boil for 10 minutes. Drain, rinse under cold water and peel. Set aside on paper towels to absorb excess water.
In a food processor, combine the basil leaves, whole pine nuts, Parmesan, garlic cloves, and 1/2 cup olive oil. Blend until smooth. Set aside.
Cover each boiled egg with one-quarter of the turkey by pressing the meat around the eggs.
Place the beaten eggs in a bowl. In a separate bowl, combine the breadcrumbs, flour, salt, black pepper, cayenne, garlic salt and chopped pine nuts.
Heat the remaining 1/2 cup olive oil over medium-high heat in a large skillet.
Dip each turkey-covered egg first in the eggs and then in the breadcrumbs, making sure the entire egg is encrusted with the crumbs.
Fry the eggs in the hot oil, cooking 3 to 4 minutes each side, turning them in the pan to make sure the entire egg has been cooked.
Once the exterior part of the eggs are brown, place on a paper towel to remove excess fat, and transfer to a plate. Drizzle the eggs with the pesto sauce and garnish with basil leaves.
This recipe was created by a contestant during a cooking competition. The Food Network Kitchens have not tested it for home use, therefore, we cannot make any representation as to the results.