Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a separate large bowl, cream together the butter and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, then stir in the vanilla extract.
Gradually mix in the dry ingredients, alternating with the sour cream, until just combined.
In a small bowl, toss the diced apples with cinnamon and walnuts.
Spread half of the batter into the prepared pan, then top with the apple mixture.
Spread the remaining batter over the apple mixture.
In a small bowl, mix together the brown sugar and additional cinnamon. Sprinkle over the top of the cake.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.