In a large bowl, cream together the granulated sugar with 4 tablespoons of butter until the mixture resembles snow.
Add the egg and the vanilla extract to the bowl, and mix until well combined.
In a small bowl, whisk together the flour with the baking powder. Alternate adding the flour mixture to the batter with the milk, mixing well after each addition.
In a separate medium-sized bowl, mix together the brown sugar and cinnamon. Melt the remaining 2 tablespoons of butter, then add it to the brown sugar mixture, and mix until well combined.
In the prepared pan, add the cake batter, then sprinkle the brown sugar mixture on top of the cake batter.
Bake in the preheated oven for 30 to 35 minutes, until a toothpick inserted in the center of the cake comes out with a few crumbs.