Preheat the oven to 350 °F (175 °C). Butter, flour, and line with parchment three 6x2-inch (15x5-cm) round cake pans (Wilton on Amazon)
Sift together (or whisk) the flour, baking powder, cinnamon, ginger, nutmeg, baking soda, and salt. Set aside
In a separate large bowl, whisk together the canola oil, brown sugar, sour cream, orange zest, and vanilla until very well blended.
Add the flour mixture to the bowl with the wet ingredients and fold everything together until the flour has almost completely disappeared.
Fold in the carrots.
Divide the mixture between the three pans, banging the pans to release any air pockets. Smooth the surfaces of the cakes with an offset spatula and bake them until they are done: a cake tester inserted in the centre of the cakes will come out clean, and the edges will have pulled away from the sides of the pan. This takes 25 to 30 minutes.
Let the cakes cool 10 minutes before unmoulding to cool completely on a wire rack.
To make the cream cheese frosting
In the bowl of an electric mixer fitted with the paddle attachment, cream together the icing sugar and the butter until it is creamy and light.
Add the cream cheese, the vanilla bean paste, and the orange zest (if using) and beat the frosting until it is smooth.
Peel off the parchment from the cake layers and place the first layer on a cake stand. Top with a couple spoonfuls of frosting (~150 grams) and smooth it out. Stack on the second cake layer and another 150 grams of frosting, then top with the final layer. Use a bench scraper or an offset spatula to smooth the sides if desired.
Chill for 30 minutes to set the frosting before serving.
Notes
If you aren't sure how to check if your cakes are done baking, you can use a cake tester or even a digital thermometer to double check that the internal temperature is around 100 ºC (212 ºF).