Preheat the oven to 180ºC. Grease a cake pan with butter and dust it with flour. Shake the pan to cover the bottom and sides, then tap it on the counter to remove the excess flour.
In a bowl, sift together the flour, salt, and baking powder. Mix and set aside.
Wash and peel the carrots. Discard the top. Cut each carrot into small slices and transfer them to a blender — slicing the carrots makes them easier to blend.
Add the oil to the sliced carrots. In a small bowl, crack each egg one by one and transfer them to the blender.
Add the sugar and blend everything well until smooth, for about 5 min.
Transfer the liquid mixture to a large bowl and add the dry ingredients in three batches, sifting them as you go. Gently mix with a whisk after each addition until well incorporated.
Transfer the batter to the prepared pan and bake for about 45 minutes. To check if the cake is ready, insert a toothpick into the center: if it comes out clean, the cake is done; if not, bake for a few more minutes.
Remove the cake from the oven. Let cool for 10 minutes before removing from the pan. Finish cooling completely before topping with icing.
For the icing
Add all the ingredients into a small saucepan, and bring it to medium heat. Keep stirring until it starts to bubble.
Drop the heat and keep stirring until it starts thickening. That is when you run the spoon or spatula on the bottom of the pan and it takes a while for the mixture to recombine.
Take off the heat to cool for a moment before smearing on the top of the cake.
