Preheat the oven to 350°F. Line a cupcake liner with cupcake liners.
To make the batter: Grate the carrots using a fine grater and add into a large mixing bowl.
Add the canola oil, light brown sugar, cane sugar, and eggs.
Mix on low until combined.
Add in the flour, baking powder, salt, cinnamon, and nutmeg.
Scoop cupcake batter into the cupcake pan, fill them three-quarters full.
Bake for 20 minutes or until a wooden pick inserted in the center comes out clean. Allow to cool completely in the cupcake pans.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cream cheese, powdered sugar, and vanilla extract.
Mix on low to combine, then speed mixer up to high for 2 to 3 minutes or until light and fluffy. Make sure to scrape down the sides of the bowl part way through mixing to ensure you have a smooth frosting.
Transfer to a piping bag with Ateco tip #808. Frost cupcakes by piping a large dollop on top.
Store under a cake dome or in an airtight container in the fridge for up to 3 days.