Preheat the oven to 350ºF. Spray a 9-inch springform pan generously with cooking spray.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and ½ cup sugar together until fluffy, about 3 minutes. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla.
In a medium mixing bowl, combine the flour, baking powder, cinnamon, and salt. Add to the wet ingredients along with the milk and beat until combined. (The batter will be thick.) Stir in the apples. Pour the batter into the prepared pan, smooth the top, and sprinkle with 2 tablespoons sugar.
Bake for 45 minutes or until golden brown and a toothpick inserted into the center comes out clean. Let cool for 20 minutes before removing the cake from the pan. The cake can be served warm, at room temperature, or cold. Place on a serving platter and serve with the custard sauce.
Make the custard sauce:
In the bowl of an electric mixer fitted with the whisk attachment, combine the egg yolks and sugar. Beat until light and fluffy, about 3 minutes.
Heat the milk in a small saucepan until it just begins to bubble. With the mixer on, slowly pour the hot milk into the egg yolk mixture, beating continuously. Once combined, pour the mixture back into the saucepan and cook over medium heat, stirring, until the mixture thickens, about 4 minutes. It should coat the back of a spoon but not be too thick. It should be pourable. Stir in the vanilla. Pour the sauce into a small pitcher and serve with the cake. (The sauce can be stored in the refrigerator until serving time.)