Preheat oven to 350F. Line two cookie sheets with silpat or parchment paper.
Place pecans on one of the prepared pans and bake for 5 - 6 minutes, until lightly toasted. Remove from the oven and set aside to cool. This step is optional, but does add flavor to the finished cookies.
Cut off root end of carrot, wash and pat it dry. No need to peel. Chop and place carrot pieces in a food procesor or blender and pulse several times until finely grated. Measure out into a 1 cup measuring dish. Set aside.
In a mixing bowl combine the vegan butter and sugars and beat on medium speed until combined. Use a spatula to scrape down sides of bowl and then beat on medium speed until light and fluffy. Add ground flaxseed, vanilla and milk. Beat again for up to one minute. Set aside.
In a separate bowl stir together the flour, baking soda, baking powder, spices, and salt.
Add rolled oats to a blender and pulse until it resembles a course flour, leaving some larger bits of oats in the mixture. Add the pecans and pulse a few more times until the pecans are broken down into small bits. Add the oats/pecan mixture to the flour mixture. Stir to combine. Pour the flour/oats mixture into the mixing bowl with the butter mixture. Beat on medium speed until just combined.
Add the shredded carrots to the batter. Stir until just combined.
Use a cookie dough dispenser to distribue cookie dough batter in balls roughly 2" apart on the prepared baking pans. Use a spoon to lightly flatten the tops of the cookie dough balls.
Bake 12 - 14 minutes, until the cookies turn a golden brown. Slightly underbaked cookies are preferred because they stay soft on the inside. Once done, remove pans from the oven and allow the cookies to cool slightly on the pan before transferring cookies to a wire rack to cool completely.