Preheat oven to 350 degrees.
Whisk together the flour, oats, soy, soda and salt.
In a separate bowl with a hand mixer, cream together the butter, sugar, eggs, and peanut butter. Mix until smooth.
Add flour mixture in several batches, mixing until just combined.
Cover with plastic and refrigerate dough for about 30 minutes.
With a large spoon, drop scoops of dough onto a baking sheet lined with parchment paper. Space the cookies about 1 1/2 inches apart, as they will expand in the oven.
Press each dough ball gently with a fork, to create the classic cross-hatch peanut butter look.
Bake about 14-16 minutes.
Transfer to a wire rack and cool completely…though they are delectable to eat when warm. Cookies can be stored in an airtight container for up to 3 days--if they make it that long in your house! :)