Start by peeling the carrots to remove the tough outer layer and then finely grating them until you have ¾ cups. Set aside.
Add the dry ingredients to a large mixing bowl, including the flour, brown sugar, cane sugar, baking powder, cinnamon, nutmeg, and salt. Whisk together until well mixed.
Cut the cold vegan butter into chunks. Then, add it to the bowl of dry ingredients and use a pastry cutter to "cut" the butter into the dough until you have a crumbly mixture. You can also use a fork to do this step, though it will take longer.
Next, add in the oat milk, grated carrots, and vanilla. Use the pastry cutter or your hands to combine into a shaggy dough. The shaggy dough will be somewhat flaky and crumbly, yet still stick together when pressed.