In a medium bowl, mix together the lunchmeat, water chestnuts, green onions, parsley, hard-cooked eggs, pepper, and oyster sauce. Set aside.
On a clean flat surface, such as a cutting board, lay out 4 to 6 wonton skins at a time. Place a tablespoon of the meat mixture into the center of each one. Keep a small bowl of water next to the work area to dip fingers in. Use wet fingers to moisten the corners of each wrapper. Quickly pinch all 4 corners together to seal in the filling. If it doesn't hold, use more water. Keep filled wontons covered with plastic wrap to prevent drying while the others are made.
Heat one inch of oil in a deep heavy skillet over medium-high heat, or heat recommended amount of oil in a deep-fryer to 365 degrees F (185 degrees C). Fry wontons for a few minutes on each side, or until golden. Remove to paper towels to absorb excess grease. Enjoy the grinds!