To make the dough, add the room-temperature vegan butter, white sugar, and brown sugar to a mixing bowl. Then, use an electric mixer to cream the butter and sugar together until fluffy (about 2 minutes).
Next, add in the shredded carrots, flax egg, and vanilla bean paste and mix together for about 20 seconds.
Then, add in the all-purpose flour, rolled oats, cinnamon, baking soda, nutmeg, and salt. Make sure to add the flour first and then add the other ingredients on top. Then, mix everything together until a thick cookie dough forms.
Cover the bowl of dough with plastic wrap and add to the fridge to chill for 1 hour. The dough can also be refrigerated for up to 24 hours.