Classic Carrot Cupcakes with Cream Cheese Frosting

For Cupcakes
Preheat the oven to 350° and line 10 muffin cups with paper liners.
In a medium bowl, whisk the flour with the cinnamon, baking soda and salt. In a large bowl, using an electric mixer or whisk, 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.
For Frosting
In a separate bow, add the softened butter and cream cheese and beat it with an electric whip. Once it is creamed, add powdered sugar and whip until light and fluffy. Add the baileys cream and little vanilla extract. Mix.
Fill a pastry bag fitted with a ½-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.