The Flying Fingers Technique
When a recipe calls for unusually thin slices of meat, I use and recommend the "Flying Fingers" technique. To slice a strip of meat across the grain into 1/8" to 1/4" thin slices:
Use the palm of your hand to hold the meat to the cutting board, extend your fingers up, only your palm should be in contact with the meat! Slide the cleaver or knife about 1/8" above the cutting board through the meat while maintaining pressure with your palm. Repeat until the meat is all sliced.
This technique is referred to as the "flying fingers" due to the appearance of the hand while cutting.
I've been doing this for years and never cut myself. The cleaver or knife must be SHARP. Note: DO NOT AT ANY TIME ALLOW ANY PART OF YOUR HAND TO TOUCH THE CUTTING BOARD!
Source "The Chinese Recipe Book" privately published April 1, 1993