Preheat the oven to 325 degrees.
In a small bowl mix together brown sugar and cinnamon, set aside.
In a bowl mix together the butter and sugar until creamy, then whisk in the egg until fluffy.
In a bowl sift together flour, baking powder, baking soda, and a pinch of salt.
Mix the dry ingredients with milk. Add vanilla and mix well.
Spoon 1/3 of the batter into an appropriately sized baking dish. Sprinkle with 1/2 of the cinnamon sugar mixture. Spoon another 1/3 of the batter on top, then remaining cinnamon mixture and then top with the remaining batter. Bake for approximately 30 - 40 minutes or until a toothpick comes out clean and dry.
Remove from oven and let cool before serving.