Preheat oven to 350℉. Line a 9x5 inch loaf pan with parchment paper.
In a blender pulse together the carrots, eggs, sugar and oil for 3 minutes or until completely smooth. Add in the vanilla, apple cider and pulse for 30 seconds.
In a large bowl, sift the flour, arrowroot powder, baking powder, salt and whisk together until combined. Next, pour in the carrot mixture and mix together until JUST incorporated. Transfer batter to the loaf pan and tap the pan a little bit on the counter to remove bubbles. Bake for 50-55 minutes or until toothpick comes out clean. Allow to set in the pan 10 minutes and then transfer to a wire rack to cool completely before frosting it.
Brigadeiro:
In small bowl, whisk together the melted butter and cacao powder until smooth. QUICKLY add in the maple syrup and whisk until smooth. Spread on the top of the cake.