Preheat the oven to 350° and line 14 muffin cups with paper liners. Spray the liners with vegetable-oil spray.
In a medium bowl, whisk the flour with the cinnamon, baking soda and salt. In a large bowl, using an electric mixer, beat the eggs with the canola oil. Gradually beat in the sugar at medium-high speed and beat until thick, about 3 minutes. Beat in the vanilla. Fold in the dry ingredients with a rubber spatula, then fold in the carrots.
Spoon the batter into the muffin cups and bake for 25 to 30 minutes, until a toothpick inserted in the center of the cupcakes comes out clean. Let cool slightly, then transfer the cupcakes to the freezer to chill.
Fill a pastry bag fitted with a 1/2-inch plain tip with the Cream Cheese Frosting. Pipe the frosting onto the carrot cupcakes and serve. Alternatively, use a knife to spread the frosting on the cupcakes and serve.
In a bowl, using an electric mixer, beat the butter with the cream cheese until smooth. Beat in the vanilla and confectioners' sugar, then beat at high speed until the frosting is light and fluffy.