Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Set aside.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time to the butter-sugar mixture, mixing well after each addition. Stir in the vanilla extract.
Gradually mix the dry ingredients into the wet mixture until just combined.
Fold in the diced apples, ensuring an even distribution throughout the batter.
Pour the batter into the prepared baking pan and smooth the top with a spatula.
In a separate bowl, combine brown sugar, oats, nutmeg, and butter for the crumb topping.
Sprinkle the crumb topping evenly over the batter.
Bake for 45-50 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for about 10 minutes before transferring it to a wire rack.
While the cake cools, prepare the cinnamon drizzle by whisking together heavy cream, powdered sugar, and cinnamon.
Drizzle the cinnamon mixture over the cooled cake.
Slice and serve your apple crumb cake warm or at room temperature.