Preheat the oven to 350°F. Grease a 9-inch round cake pan.
Streusel Topping: In a small bowl, mix the streusel topping ingredients together until it forms a wet, crumbly mixture. Set aside.
Apple Filling: In a bowl, toss the chopped apples with cinnamon and brown sugar. Set aside.
In a medium mixing bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt. Set aside.
In a separate mixing bowl with an electric hand whisk (or in the bowl of a stand mixer with the paddle attachment) beat the softened butter, brown sugar, and granulated sugar until it is fluffy. Beat in the egg & vanilla extract. Then add the milk and mix again. (It’ll probably look split at this point, but that’s normal - it’ll all come together in the next step.)
Add the flour mixture to the butter mixture. Mix on a low speed until you no longer see dry pockets of flour. Scrape the sides and bottom of the bowl to ensure everything is well-mixed.
Set aside ½ cup of the chopped apples and gently fold the rest into the cake batter.
Spread the cake batter into the prepared cake pan. Spread the reserved chopped apples on top, then sprinkle the streusel evenly on top.
Bake for about 40 to 50 minutes, until a toothpick or knife inserted into the center of the cake comes out clean. Allow the cake to cool for 10 minutes, then remove it from the pan to finish cooling.
While the cake cools, mix the sifted powdered sugar, milk, vanilla, and salt in a small bowl until it forms a smooth glaze. Drizzle on top of the cake & allow it to drip down the sides. Enjoy!!