In a small bowl or a microwave-safe mug, combine the melted butter, brown sugar, vanilla, milk, flour, baking powder, and cinnamon. Stir or whisk to combine the ingredients until smooth. Fold in the shredded carrots.
Microwave the mug cake for 1 to 1½ minutes. In my microwave, it's best at 1 minute 15 seconds. Begin checking at 1 minute though. The cake should look set but be careful not to over-microwave.
Let cool before topping with whipped cream, cream cheese glaze or simply powdered sugar.
Notes
Add-ins: Readers have also enjoyed adding a small amount of raisins and chopped nuts like walnuts or pecans. You could also add a small pinch of nutmeg if desired.
Topping Ideas: If you want a topping for your mug cake, whipped cream, confectioners' sugar, or an easy cream cheese frosting (recipe below) is delicious!