Cream the brown butter and light brown and granulated sugars together on medium speed. On low-medium speed, beat in the egg, yolk and vanilla extract about 20 seconds before adding the next. Gently fold in the shredded carrots.
On the lowest speed setting or by hand, mix the dry ingredients to the wet until just combined. Stir in the oats until just combined. Cover the carrot cake cookie dough to chill in the fridge for 2 hours.
Preheat the oven to 375 F (190 C) for about 20-30 minutes before baking the cookies. Scoop about 2 tablespoons (30 g) cookie dough, roll them into balls and place them on the baking sheet. Bake the cookies for 10-14 minutes.