Preheat the oven to 350°F. Prepare two large baking sheets with parchment paper.
In a medium sized bowl, combine 2 tablespoon ground flax seeds with 5 tablespoon warm water. Stir and let rest for 3-5 minutes. In the meantime, you can prepare and measure other ingredients.
Stir the peanut butter before measuring it out. To your bowl add 1 cup peanut butter, ½ cup maple syrup, ½ cup coconut sugar and 1 tsp vanilla. Stir thoroughly.
To your bowl add remaining ingredients (except the pure cane sugar); 1/2 cup oat flour, 1/2 cup gluten free flour, 3 tablespoons arrowroot starch, 1 teaspoon baking soda, 1/4 teaspoon sea salt. Stir to combine until just mixed. Do not over stir.
Using a 1 ½ tablespoon scoop, measure out the dough and roll into balls. I am just a smidge generous while scooping. Roll each ball in the pure cane sugar and place each one on the cookie sheet, dividing them between the two sheets.
Press each cookie flat and make a crisscross pattern on top. To do this, dip a fork in a small bowl of warm water, shake off excess and press onto top of cookie. Press it again with the fork crosswise. Make sure you are doing a good job shaking off the excess water so there is not a lot of excess moisture sitting on top of each cookie.
Place in oven for 15 minutes. If you like very soft, delicate cookies, bake for 13 minutes. Remove from oven and let cool on baking sheet for 5-10 minutes, then move to a cooling rack. Store in a sealed container on the counter for up to 3 days or in the fridge for up to a week. They can also be frozen for up to 3 months.