Line a 9-inch (22.5 cm) square baking pan with parchment paper, allowing paper to overhang on the sides (for removal of the shortbread).
In a medium bowl, whisk together the oat flour, potato starch and salt.
In a large bowl, cream together (I used a wooden spoon) the vegan butter and coconut sugar until blended and somewhat fluffy. Add the oat flour mixture, stirring until combined (it may look slightly crumbly).
Very firmly press dough evenly and firmly into prepared pan. Use a small flat bottomed tray, or measuring cup, to tamp down the dough. Prick with a fork.
Loosely cover with plastic wrap and chill at least 1 hour or up to 1 day.
Preheat oven to 325F (160C).
Bake in the preheated oven for 40 to 45 minutes until shortbread is pale golden. Cool completely in pan.
Using paper overhang, carefully remove shortbread from pan; place on cutting board. Cut into 4 quarters; cut each quarter in half, then in half again, making 16 rectangles total.
Notes
Potato Starch Substitutions: An equal amount of rice flour, cornstarch or arrowroot can be used in place of the potato starch.Butter Options: If you eat dairy, feel free to use 2 sticks of butter in place of the margarine.Sugar Options: An equal amount of the brown sugar or granular sugar of your choice can be used in place of the coconut sugar.Oat Flour Tip: You can grind your own oat flour in a high-speed blender or other blender. It will take about 1.25 cups of rolled oats to yield 1 cup of oat flour. Note that a food processor will not grind the oats into a fine enough flour.Coconut Oil Shortbread: Add the coconut sugar to the oat flour mixture in step 2. Add 1 cup melted coconut oil to the oat mixture, stirring to combine. Press into prepared pan and place in freezer for 30 minutes to harden. Proceed with remaining steps.