Preheat oven to 350°F and prepare 4 6" cake pans with grease and parchment on the bottom. Set aside.
In a medium bowl, whisk dry ingredients together. Set aside.
In a separate large bowl, whisk vegetable oil, light brown sugar, granulated sugar, eggs, and vanilla bean paste together. Then whisk in the sour cream to the wet mixture, followed by the grated carrots. Add the dry ingredients to the wet ingredients and mix until just combined.
Distribute evenly into pans and bake for ~35 minutes, or until a toothpick comes out mostly clean (except a few crumbs). Remove and set aside to cool for 15 minutes in the cake pans before transferring to a cooling rack to cool completely.
Use a sharp serrated knife to cut the domes off the top of each cake, and crumble the cake scraps onto a parchment-lined sheet pan. Continue baking these at 300°F for ~30 minutes, or until crunchy. Remove from oven and set aside.