Preheat oven to 350 degrees. Lined cookie sheets with parchment or silpat. (note silpats retain heat, check cookies a minute or two earlier.
In a small bowl, combine the flour, baking soda, and salt, using a whisk.
Cream the butter and sugars together in the bowl of a stand mixer for 1-2 minutes until well combined. Batter should be smooth and creamy not fluffy which would give you cakey cookies. Use the paddle attachment.
Add the peanut butter, egg, and vanilla. Mix well and scrape the bowl.
Add flour mixture to the butter mixture all at once and mix on low speed just until incorporated.
Scoop dough onto parchment-lined baking sheets about 2 inches apart. Bake at 350 degrees for 10 to 12 minutes or until just set*.
Allow cookies to cool slightly on the sheet for approximately 2 minutes before transferring them to a cooling rack. Store cookies in an airtight container.