Preheat the oven to 350° F.
Put a silpat pad (silicone pad) on a cookie sheet or parchment paper.
Mix the egg replacer and water together and set aside.
In a large bowl add the flour, baking soda and salt. Mix together.
Mix the peanut butter and syrup until well blended.
Stir in the egg replacer mixture and vanilla.
Stir the peanut butter mixture into the flour mixture. Blend well.
Roll into about 48 balls and then place some on a cookie sheet about 2" apart.
Flatten each ball slightly with the back of a fork to give the traditional peanut butter cookie cross hatch design.
You will need to dip the fork in water every once in a while to keep it from sticking.
Bake 10 to 12 minutes.
On your last 1/3 of the dough you could mix in the walnuts before rolling if you want some with nuts.