Chef John's Carrot Cake
You can substitute vegetable oil for the coconut oil. If you do go with the coconut oil, you can use a 'virgin' coconut oil, which will have a fairly strong coconut aroma, and identifiable flavor, or you can go with a more refined coconut oil, which is virtually odorless and flavorless. I used the latter, but the former would be fine, if that's what you're into.
Use more carrots for a moister cake.
Divide batter between two 9-inch round pans if you want to make a layer cake.