1Preheat oven to 350 degrees F (175 degrees C). Grease a 10-inch cake pan and dust with flour.
2Combine 2 cups sugar, eggs, vegetable oil, and carrots in a blender; blend until very smooth, about 5 minutes.
3Pour carrot mixture into a bowl; add flour and baking powder. Mix well to combine. Pour into the prepared cake pan.
4Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 40 minutes. Cool in the pan for 5 minutes. Invert onto a wire rack to cool.
5Combine 1/2 cup sugar, cocoa powder, milk, and butter in a small saucepan over low heat. Cook, stirring constantly, until sauce begins to bubble and thicken, 3 to 4 minutes. Remove from heat and quickly spread over cake.
Footnotes
Cook's Notes:
I've also tried adding the flour and baking powder to the blender and mixing the batter that way, but it depends on the blender.
Substitute powdered chocolate drink mix (such as Nesquik(R)) for the cocoa powder if desired, but reduce sugar by 1 tablespoon if doing so.
Any kind of chocolate frosting goes well with this cake. Try chocolate ganache!