Preheat your oven to 350°F (175°C) and prepare a bundt or cake pan.
In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Beat until light and fluffy.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt.
Gradually add the dry mixture to the wet mixture, alternating with the milk. Mix until just combined.
Fold in the diced apples gently until evenly distributed.
Pour the batter into the prepared pan and smooth the top. Bake for 45-50 minutes or until a toothpick inserted comes out clean.
Let the cake cool in the pan for 10 minutes before inverting onto a wire rack.
While the cake cools, prepare the custard sauce by heating 2 cups of milk in a saucepan over medium heat.
In a separate bowl, whisk together the egg yolks and 1/2 cup sugar until well combined.
Gradually add the heated milk mixture to the yolk mixture, whisking continuously to temper the eggs.
Return the custard mixture to the saucepan and cook over low heat, stirring constantly until it thickens.
Remove the custard from heat and stir in the vanilla extract. Let cool slightly before serving.
Slice the cooled apple cake and serve with a generous drizzle of custard sauce.