01 - Preheat oven to 350°F. Grease and flour a 9-inch round cake pan.
02 - Whisk together flour, baking powder, cinnamon, nutmeg, and salt in a medium bowl.
03 - In a large bowl, cream the butter and sugar until light and fluffy. Beat in the eggs one at a time, then mix in the vanilla.
04 - Alternately add the flour mixture and milk to the butter mixture, beginning and ending with flour. Mix until just combined.
05 - Gently fold in the apple slices. Spread the batter evenly into the prepared pan. Mix 2 tablespoons sugar with ½ teaspoon cinnamon and sprinkle over the top. Bake for 50-55 minutes, or until a toothpick inserted in the center comes out clean.
06 - Cool in the pan for 10 minutes, then turn out onto a wire rack.
07 - In a saucepan, heat the milk until just simmering.
08 - Whisk egg yolks, sugar, and cornstarch in a bowl until smooth.
09 - Gradually whisk the hot milk into the yolk mixture, then return to the saucepan. Cook over medium-low heat, stirring constantly, until the custard thickens, about 5 minutes. Do not boil.
10 - Remove from heat and stir in vanilla extract. Serve the cake warm or at room temperature with the warm vanilla custard poured over each slice.