In a medium bowl, combine the light brown sugar, all-purpose flour, and cinnamon. Cut in the butter until the mixture resembles coarse crumbs. Set aside.
Preheat oven to 375 degrees F. Grease an 8-inch square baking pan with butter or cooking spray.
In a large bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy. Beat in the egg and vanilla extract until well combined. In another bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add to the butter mixture, mixing until just blended.
Spread half of the batter evenly into the prepared pan. Sprinkle with half of the crumble topping. Spread the remaining batter over the top. Sprinkle with the remaining crumble topping. Bake for 10-12 minutes, or until golden brown and a toothpick inserted into the cake comes out clean. Let cool for at least 10 minutes before serving.