Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.
In a large bowl, cream the butter and sugar together until light and fluffy.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla.
Gradually add the dry ingredients, alternating with the milk. Mix until just combined.
Fold in the chopped apple.
Pour the batter into the prepared pan and smooth the top.
For the topping: Mix brown sugar and cinnamon, then sprinkle over the cake batter.
Bake for 35-40 minutes, or until a toothpick inserted comes out clean.
Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.