Grease a mug with cooking spray or butter and set aside.
In a small bowl, whisk the melted and slightly cooled butter with the sugar until smooth, then add in the milk, egg yolk, and vanilla.
2 tbsp unsalted butter, 2 tbsp granulated sugar, 1 tbsp milk, 1 large egg yolk, ½ tsp vanilla extract
Whisk in the flour, baking powder, salt, and cinnamon. Fold in the grated carrots.
¼ cup all-purpose flour, ½ tsp baking powder, pinch of salt, ½ tsp cinnamon, 3 tbsp freshly grated carrots
Pour the batter into the greased mug and microwave for 60-90 seconds until fully cooked through. Allow it to cool in the mug for about 5 minutes before topping with icing. You could also flip it out onto a plate to cool completely.
While the cake is cooling, make the cream cheese icing by whisking together the cream cheese and powdered sugar until completely smooth and no clumps remain. If needed, add milk to get the right consistency. Top on the cooled cake and enjoy!
1 tbsp cream cheese, 1 tsp powdered sugar, 1 tsp milk