Preheat your oven to 375 degrees Fahrenheit (190 degrees Celsius) and prepare a jelly roll pan by greasing it well and lining the bottom with a piece of parchment paper. It's also a good idea to grease the top of the parchment paper.
Cream the room-temperature butter in a mixing bowl with the sugars and vanilla using a hand mixer until the mixture is soft and creamy.
Add the eggs one at a time and incorporate them well after each addition.
Add the shredded carrots and mix with a spatula.
Add the flour, spices, salt and baking powder and mix just until everything is incorporated.
Pour the batter into the prepared jelly roll pan and spread it out to the edges being careful to spread the batter as evenly as possible. Bake at 375 degrees Fahrenheit (190 degrees Celsius) for about 13-15 minutes or until a toothpick inserted into the middle of the cake comes out clean.
As the cake bakes, dust powdered sugar generously over a clean kitchen towel creating a rectangle shape, slightly larger than your jelly roll pan.
Immediately after taking the cake out of the oven, line a cooling rack with parchment paper and place it upside down on top of the hot cake before inverting. Invert it again so the cake is face down on top the kitchen towel over the powder sugar. Peel off the parchment paper from the bottom of the cake.
Roll the cake with the towel inside the roll as well, from the narrow end while it's hot from the oven. Don't roll it too tightly or aggressively, but the cake should be firmly rolled with no space on the inside of the roll.
Let the carrot cake cool, rolled, turning it several times throughout the cooling process so that it keeps a round shape and doesn't flatten on one side only.