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.