The sliced chicken breasts should be about an inch thick; if it is much thicker than that, pound it out to about an inch. Sprinkle both sides of the chicken breasts with sea salt and pepper to taste. Add a slice of ham and then the provolone. Drag a spoonful of pesto sauce down the middle. Fold over and secure the open side with a toothpick. Heat the EVOO in a large saute pan over medium-high heat. Carefully add the chicken to the EVOO and saute until golden brown on both sides, about 5 minutes on both sides. Transfer the chicken to a plate and reduce the heat to medium. Deglaze the pan with the white and a tablespoon of butter. Once the sauce begins to thicken and becomes glossy, add the chicken back into the pan. Cook on low until chicken is sufficiently warmed throughout. Discard the toothpicks. Serve immediately.