Preheat the oven to 350°F (180°C). Line one or two cookie sheets with parchment paper. Slightly oil paper. Set it aside.
In a mixing bowl, stir with a silicone spatula: oat flour with melted coconut oil, maple syrup, and vanilla if used. The dough will be sticky, and that's normal.
Place the bowl in the fridge for 10 minutes to rest the dough.
Remove the bowl from the fridge, and if the dough is too wet, knead in more oat flour to adjust. The dough will stay sticky but not runny or wet.
The easiest way to work with oat flour cookie dough is to oil your hands with coconut oil, and roll about one tablespoon of batter between your hands. Place the ball on the oiled cookie sheet and flatten it down with the palm of your hand. You can also use cookie cutters, but it's a bit more challenging - see instructions below.
Cookie-cutter option: first, oil two pieces of parchment paper and place the dough in the center of the first piece of paper, place the other piece on top of the dough, and using a rolling pin, roll the dough encased between the oiled pieces of parchment paper until 1/4-inch thin.
Oil the cookie cutters and cut out shapes. Slide an oiled flat tool under the dough to transfer it to the cookie sheet.
Remove outside dough and reroll it into a ball to reform cookies.
Bake the cookies for 7-9 minutes until golden brown.
Cool on a cooling rack before frosting with vegan royal icing.
Store in a cookie jar at room temperature for up to 1 week or freeze for later up to 3 months. Thaw at room temperature.