Preheat the oven to 375℉ (190C). Line 2 or 3 cookie sheets with parchment paper or use non-stick baking sheets.
In a small bowl, combine the flour, baking soda, and salt. Set it to the side. In a food processor or blender, whip the egg replacer and water together until thick and creamy. Side note - I use an electric hand mixer and mine has never looked "thick and creamy," but it still does the job.
In a large bowl, add the brown sugar, peanut butter, butter, milk and vanilla. Beat on medium with an electric hand mixer until well blended. Add the egg replacer mixer and beat until just blended. Add the flour mixture and blend. Add the ground peanuts and chocolate chips at the end if you choose.
Drop spoonfuls of the dough onto the cookie sheets. Flatten slightly with a fork. I like doing the criss-cross pattern.
Bake for 10 to 12 minutes or until just beginning to brown. Do not overbake. Remove from the oven and place on a cookie sheet after cooking for 3 minutes.