Preheat oven to 350° and line 2 cookie sheets with parchment paper.
In a small bowl, combine flour, oats, baking soda, and salt. Set aside.
In a large bowl, combine butter, brown sugar, and white sugar. Mix until smooth. Add in peanut butter and mix well. Stir in egg and vanilla.
Add in flour mixture and mix until completely combined.
Scoop into 26 even balls (a cookie scoop works great for this).
Bake for 20 minutes, only 6-7 cookies on a tray a time.
Repeat with remaining dough until it is all baked.
Let cool completely before filling.