Mix sugar, brown sugar, eggs, and vanilla until creamy.
Add peanut butter and mix until smooth.
Mix the baking soda with the water. It will fizz. Dump this mixture into the cookie dough.
Add the oats, sprinkle the salt evenly over the oats.
Mix to combine.
Add the chocolate chips and chopped walnuts and mix until everything is evenly combined.
Cover your cookie sheet with parchment paper or a silicone mat for easy clean up.
Drop by rounded tablepoons-full on the baking sheet, leaving plenty of space between the cookies (I used 2 cookies per row and baked 8 cookies per pan and that worked fine).
Bake 10-12 minutes, or until they turn a nice, golden brown.
Let them cool on the baking sheet for a minute or so before trying to move them to a cooling rack. They will hold together better.