To Make The Cake: Preheat your oven to 350°F (180°C). Line a 9×13 inch pan with parchment paper. In a blender or food processor, combine the chopped carrots, eggs, and vegetable oil. Blend until very smooth.
Pour the batter into the prepared cake pan. Bake in the preheated oven for about 25 minutes, or until a toothpick inserted into the center of the cake comes out with a few moist crumbs.
To Make The Chocolate Brigadeiro Frosting: While the cake is baking, prepare the chocolate topping. In a small saucepan, combine the butter, sweetened condensed milk, chocolate chips, and milk or heavy cream.
Once the cake is done and slightly cooled, pour the warm chocolate topping over the cake, covering the surface evenly, add sprinkles if desired. Allow the cake to cool completely and the topping to set before slicing and serving.