1. Heat oven to 350°.
2. In a food processor, combine 2 cups oats and walnuts and process into a very fine meal. Pulse in flax, baking powder, baking soda, and salt.
3. Add oil, syrup, and vanilla and process until combined. Transfer to a bowl; stir in remaining 1½ cups oats.
4. In batches, drop 2-tablespoonful mounds onto parchment-lined baking sheets. Bake until golden brown at edges, about 10 minutes. Let cool 2 minutes on baking sheet before transferring to a rack to cool completely.
5. To make frosting, beat all ingredients together with an electric mixer on medium-high until smooth. Add additional tapioca starch (if necessary) to reach desired consistency. As it sits, the frosting may begin to separate, just re-whip as needed.
6. Sandwich 1 tablespoon frosting between 2 cookies to make double doozy. Transfer to refrigerator for about 30 minutes to set frosting. Store in refrigerator. (See note.)

*Note: These cookies will start to fall apart if left at room temperature for over an hour. If desired, add ½ teaspoon xanthan gum to food processor along with baking soda. This will help cookies hold their shape.