Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.

In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and ground cinnamon.

Gradually add the dry ingredients to the wet mixture, alternating with the milk, and mix until just combined.

Fold in the chopped apples.

In a bowl, combine the brown sugar, flour, and ground cinnamon. Cut in the cold butter until the mixture resembles coarse crumbs.

Pour the batter into the prepared cake pan and sprinkle the streusel topping evenly over the batter.

Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.

Allow to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.