Preheat oven to 350°F (175°C) and grease a 9-inch round or rectangular cake pan.
Grate or roughly chop the carrots and transfer to a blender.
Add the vegetable oil to the blender and blend until smooth.
In a large mixing bowl, whisk the eggs and sugar until well incorporated.
Pour the carrot-oil blend into the bowl and mix thoroughly.
Add the sifted flour, baking powder, and vanilla extract, and mix until a smooth batter forms.
Pour the batter into the prepared pan and smooth the surface.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
While the cake cools, prepare the chocolate frosting by combining the sweetened condensed milk and unsweetened cocoa powder in a bowl and stirring until smooth.
Once the cake has cooled slightly, spread the chocolate frosting over the top evenly.
Allow the cake to cool completely before slicing and serving.