Preheat oven to 425 F. Spray two cookie sheets with cooking spray.
Place chicken breasts two at a time between large pieces of plastic wrap. Use a rolling pin or mallet* to pound the chicken to about 1/2" thick.
Slice chicken breasts into strips.
Add flour to a bowl or pie plate.
Transfer chicken, a few strips at a time, to the bowl of flour, coating each piece. Set aside. Discard any remaining flour.
Place panko crumbs in a bowl. In another bowl whisk together eggs and water.
Dip flour-coated chicken strips into egg mixture, then press into the panko crumbs to coat each piece. (You may need extra panko depending on the size of your chicken pieces - add more to the bowl as needed, but remember that any extra must be thrown away to prevent contamination)
Place coated chicken pieces on the prepared baking sheets.
Bake sheets one at a time, 15-20 minutes until chicken is at least 165 F in the thickest parts. It will be pale and may not look done - use a meat thermometer to prevent overcooking.