In a small bowl, whisk together the flaxseed meal and water. Let sit 10 minutes (this creates a flax “egg”). In a separate, medium bowl, whisk the brown sugar, granulated sugar, all-purpose flour, baking powder, baking soda, salt, and cinnamon until smoothly combined.
Add the peanut butter, vanilla, and flax egg. Whisk again until the dough is smooth and the peanut butter has completely blended into the batter. As the batter thickens, switch to a rubber spatula or spoon as needed. Place the dough in the refrigerator to chill for 30 minutes.
Place a rack in the center of your oven and preheat the oven to 350 degrees F. Line a large rimmed baking sheet with parchment paper.
Shape and roll the cookies: Place the sugar in a shallow bowl (a pie plate works well). Remove the dough from the refrigerator. Scoop the cookies by heaping 1 tablespoons of dough and roll into balls that are about 1 1/2 inches in diameter. Roll in the sugar, then place on the baking sheet, leaving 1 to 2 inches of space around each one. With the tines of a fork, make a crisscross indent on each, leaving the cookies fairly thick. (Return the remaining dough to the refrigerator between batches.)
Bake until the cookies are barely golden at the edges but still just a little underdone in the center, about 8 minutes. Let the cookies rest on the baking sheet for 2 minutes, then gently transfer to a wire cooling rack to finish cooling. Repeat with the remaining dough.
*I recommend using a shelf stable peanut butter that does not have to be stirred or refrigerated (natural peanut butters that separate, while delicious, can be unreliable in baking). I used Jif Natural.
Nutrition was calculated without the sugar used for rolling, as the amount will vary per cookie.
TO STORE: Keep the cookies in an airtight storage container at room temperature for up to 3 days. Vegan peanut butter cookies do stay fresh in the refrigerator, but they stay the most fresh tasting at room temperature.
TO FREEZE COOKIES: Place the cookies in an airtight freezer-safe storage container or ziptop bag in the freezer for up to 3 months. Let come to room temperature before serving.
TO FREEZE DOUGH: Prepare the cookie dough as directed, rolling it into cookie dough balls. Place the balls on a parchment-lined baking sheet, and freeze until solid. Store the frozen dough balls in the freezer for up to 3 months. Let soften in the fridge, then roll them in the sugar and press with a fork just before baking.