Place each chicken breast between 2 sheets of plastic wrap. Using the flat side of a meat mallet, pound the breasts to a 1/4-inch thickness, being careful not to tear the meat. Remove the top piece of the plastic wrap and season lightly with salt and pepper.
Insert 1 plug of truffle butter in the center of each breast. Roll the meat up and over to completely enclose the butter. Secure the meat with a toothpick.
In a shallow bowl, beat the eggs and water. In another bowl, place the flour and lightly season with salt and white pepper. In a third bowl, combine the bread crumbs and Parmesan and lightly season with salt and white pepper. One at a time, turn the stuffed chicken breasts in the flour to lightly coat, shaking to remove any excess. Dip in the beaten eggs, letting the excess drip off, then dredge in the bread crumbs to coat completely. Refrigerate until very cold, at least 30 minutes or until ready to cook.
Preheat the oven to 350 degrees F.
Heat 3 tablespoons of the clarified butter in a large, ovenproof skillet over medium-high heat. Add the chicken breasts and cook, turning, until browned on all sides, 2 to 3 minutes.