In a large mixing bowl, cream together the butter and sugars until light and fluffy then beat in the eggs and vanilla.
Add 1 1/2 cup of oats into a food processor or blender and grind into fine flour. Add the oat flour, all-purpose flour, baking soda and salt to the butter mixture then stir until combined. Add remaining oats and mix until evenly incorporated. Cover with plastic wrap and refrigerate for 30 minutes.
Preheat oven to 350 degrees and line a baking sheet with parchment paper. Form dough into 1½" balls then flatten dough in your palm until it’s approximately ¼" thick. Spoon about 1 tsp of peanut butter into center of dough.
Form cookie dough up around the filling to form back into a ball. If necessary, patch any openings with a bit of extra dough. Repeat with remaining dough.
Place the dough balls onto the cookie sheet at least 3" apart. Bake 15–17 minutes, or until golden brown around the edges and set in the middle. Remove from pan and allow cookies to cool on a rack.
One Last Thing
Add a few peanut butter chips to the top of each ball of dough before baking to make them even more scrumptious!