Preheat your oven to 350°F (175°C) and grease an 8x8 inch baking pan.

Melt approximately half a cup of butter in a microwave-safe bowl.

Add one cup of brown sugar to the melted butter and mix well.

Incorporate one room-temperature egg and a teaspoon of vanilla extract into the mixture.

Sift in one cup of all-purpose flour, one teaspoon of ground cinnamon, one teaspoon of baking powder, and a pinch of salt. Mix gently.

Fold in one and a half cups of freshly shredded carrots into the batter.

In a separate bowl, beat eight ounces of softened cream cheese and one cup of powdered sugar until smooth.

Pour half of the carrot cake batter into the prepared pan.

Drop dollops of the cream cheese frosting evenly over the carrot cake batter.

Pour the remaining carrot cake batter on top and swirl lightly with a knife.

Bake for 35 to 40 minutes, checking for doneness.

Let it cool completely before slicing into squares.