Start by preheating the oven to 350°F (180°C).
In a blender, add peeled carrots, sugar, eggs, and oil.
Blend for about 3 minutes, making sure no carrot pieces are left unblended.
Pour the batter into a bowl. Add all-purpose flour and baking powder, stirring until there are no dry spots left. Be careful not to overmix, as overmixing can make the cake tough.
Grease a 9x13 inch baking sheet. Pour the batter into the baking sheet and bake for 25-30 minutes. To test for doneness, insert a toothpick into the center of the cake: it will be ready when it comes out with only a few crumbs sticking to it, or clean.
You can wait for the cake to cool, or you can make the chocolate frosting right away. This frosting will harden after it cools.
For the chocolate frosting, in a saucepan, add butter, cocoa powder, sugar, and milk.
Using low heat, let it simmer for 5 to 10 minutes, or until the chocolate mixture thickens and bubbles. Stir the mixture throughout the process.
Pour the frosting while hot over the cake. Wait for it to set before slicing.