Heat oven to 375℉/190℃.
Line sheet pan with parchment paper. Set aside.
In a large bowl, whisk together oat flour, all purpose flour, baking powder, baking soda, and salt. Set aside.
With an electric mixer, beat butter and sugar.
Add eggs, one at a time, beating well after each.
Mix in vanilla.
Stir in flour mixture just until blended.
Divide dough into thirds.
Working with 1 portion of dough at a time, place on an un-floured piece of parchment.
Lightly sprinkle top with flour.
Roll into a rectangle that is 4-inches wide and 1/8-inch thick.
Trim, if necessary.