Preheat the oven to 350°F and line a muffin tin with paper cases.
In a large bowl, beat sugar, canola oil, eggs, sour cream, applesauce, and vanilla until well combined. Set aside.
In a medium bowl, sift together the flour, spices, baking powder, baking soda, and salt. Whisk to combine. Set aside.
Add the dry ingredients to the wet and mix until just combined. Some specks of flour are fine. Add the carrots. Gently fold until combined.
Use a scoop to evenly portion out your batter. You will have enough to make 10 cupcakes. Bake for 20- 22 minutes, or until the cupcakes spring back when poked and a skewer comes out clean.
Cool in the pans for 5- 10 minutes, then transfer to a cooling rack to cool completely.
Cream Cheese Frosting
In a stand mixer fitted with a paddle attachment, beat the butter until smooth and light, about 4 minutes. Scrape the bowl down and add the cream cheese. Beat until combined and light, another 4 minutes.
Add about one third of the powdered sugar. Beat for 1- 2 minutes, starting on low and bumping up to medium. Add another third of the sugar. Beat for another minute. Add the remaining powdered sugar and vanilla. Beat for a minute or two until combined and fluffy.
Assembly
Pipe cream cheese frosting onto the cupcakes once cooled. Cream cheese frosting should only be at room termperature for 4 hours or less. Place cupcakes in the firdge if you will not be serving within that time frame. You will have extra frosting.
Notes
There is enough frosting for roughly 16 cupcakes, more or less.