Preheat the oven to 375 degrees F (190 degrees C, or gas mark 5). Line cookie sheets with parchment paper or use 2 non-stick cookie/baking sheets.
In a small bowl, combine the flour, baking soda, and salt. Set aside. Whip the egg replacer and water together in a blender or food processor, until thick and creamy.
In a large bowl, combine the brown sugar, peanut butter, butter, milk, and vanilla. Beat at medium speed with an electric hand mixer, ground peanuts, if using, and chocolate chips, if using, and mix until just blended.
Drop by rounded tablespoons 2 inches (5cm) apart onto the ungreased cookie sheet. Flatten slightly in a criss-cross pattern with the tines of a fork.
Bake for 10-12 minutes, or until set and just beginning to brown. Do not overbake. Remove from the oven and let the cookies cool on the sheet for 3-5 minutes before removing to let cool on a wire rack.
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