Preheat the oven to 350ºF or 180ºC.
Prepare the flax egg by mixing the ground flaxseed with the water, and let the mixture rest at room temperature for at least 5 minutes.
Add the vegan butter, peanut butter, sugar, and vanilla extract to a large bowl and beat until light and fluffy using a hand mixer or a stand mixer fitted with a paddle attachment.
Add the vanilla and flax egg and beat on low speed until just incorporated.
Combine the dry ingredients in a medium mixing bowl (flour, baking powder, baking soda, and salt).
Incorporate the dry ingredients and beat on low speed until combined. If the dough is tough to stir, using your hands to mix it together will be easier.
I used a cookie scoop to make my cookies, but feel free to use a regular spoon or even your hands.
Fill the scoop with dough and just press and release onto a lined baking sheet.
Roll the dough into balls, then roll the balls in sugar and place them evenly onto the baking sheet, about 2 inches apart (about 5 cm).
Using the back of a fork, flatten in a crisscross pattern.
Bake for 10-15 minutes or until the cookies are very lightly golden brown (I baked my cookies for 12 minutes). They will be soft when they come out of the oven but will firm up as they cool.
Remove from the oven and cool the cookies on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.