Preheat oven to 350°F. Grease or line 2 baking sheets with parchment paper.
In large bowl, using a hand whisk or stand mixer, cream together the vegan butter, peanut butter, and sugars until fluffy. Add the vegan egg and vanilla extract and whisk until combined.
In a small bowl, mix together the flour, baking soda, and salt. Add the dry ingredients to the wet ingredients and mix with a spatula or wooden poon until everything is combined and forms into a dough.
Roll 1 tbsp of dough for each cookie and place on prepared baking sheet. Press down to flatten, then press a fork down horizontally and then vertically to make a grid pattern on the top of the cookies.
Bake for 18-20 minutes, until the bottoms become a light golden brown.
Let the cookies cool about 5 minutes before transferring them onto a wire rack to finish cooling.