Hi welcome to my super cool recipe for carrot cake. Here in Brazil we make carrot cake a little different than in other countries. Our carrot cake is orange (like a carrot) and has a chocolate coating (I think that's the term? It's not frosting I don't think. It's got melted chocolate on top.)
I forgot to take a picture of the finished cake when I made it but here's a picture I stole from a recipe website:

Credit: https://www.tudogostoso.com.br/receita/23-bolo-de-cenoura.html
Anyway, onto the recipe!
(About the measurements: The cups I used were about 150 ml, and the recipe worked)
Main cake dough:
Chocolate:
The first step is, shredding the carrots. You can do this by just shredding normally, or by juicing them if you have a way to do it. But essentially, you need to turn the carrots from solid to liquid in some way. I shredded them because it makes them easier to blend later. And of course, you should wash them and peel them before doing this, but you knew that already didn't you?

Now that you have shredded them, put them in a blender. Add the Eggs and the Oil. If this looks gross to you then I have some news about how every cake you've ever eaten was made.

After you've blended them, you should have some Carrot Slop. Pour the slop into a bowl. It should look like this, with no huge bits of carrot anywhere:

Add the Flour and the Sugar to the slop, and then mix it with a wooden spoon until it's homogenous. Or put it in a mixer if you find that easier, idk. Finally, put the Baking Powder and mix it again. I don't know if mixing it last makes any difference than if you just mix them all at once, but my mom always told me to mix the baking powder last so that's what I do.
Pour your mix into a baking tray. Here I've put it on baking paper but usually we'd just grease the tray with butter and flour, so if you don't have baking paper then that's the way to go!

Put it in the Oven, which should have been preheated for around 10 minutes, at 200° C (392° F? At this point just round it to 400 idk). Leave it in the oven at that same temperature, for 30 minutes.

Before you take the cake out of the oven make sure to stab it with a woodpick to make sure it's actually cooked all the way. The woodpick should come out clean. If it's not ready yet then leave it for longer until it's done. Here's what it looks like when I took it out of the oven:

Get a cooking pot, and put it on the stove at a low heat. First, put the Butter and the Milk, and mix them until the butter melts. Then you can add the Sugar and the Cocoa Powder. Mix it until it looks uniform.
I used 100% cocoa, but you can use 70% or 50% too. You'll just need to put less sugar to compensate for it.

The chocolate coating should be mostly liquid for now. As you let the cake cool down, it will get a little firmer. Now that you have the coating done, go back to the cake and stab it with a fork a bunch of times. This will make sure some of the coating gets inside the cake, which I guess makes it not a coating?
And now the cake is done! It's not very hard to make, as you could probably gather.

This is my shitty phot I took of it. This was right after I put the coating, so it's still very hot and liquid. I put it in the fridge to cool, it tastes a lot nicer in my opinion :)
Anyway I hope you enjoy the cake!
When I was a kid, like maybe 4 or 5, I used to hate carrot cake. I had never eaten it, but I knew that carrot = vegetable and that's yucky. Then one day at school they served us a Mystery Cake, and everyone loved it! Our teacher said: "So, do you guys know what kind of cake it was? :)" and we tried to guess different things, like chocolate or vanilla. But the teacher revealed that it was carrot cake, and everyone felt so betrayed... but not me. I realized that you can't say you hate something if you've never even eaten it!
Carrot Cake has been my favorite flavour of cake ever since that day.
So thank you Teacher and Lunchlady, for serving me the Mystery Cake.