01 - Preheat oven to 350°F. Grease and flour a 9-inch round cake pan, ensuring even coverage to prevent sticking.
02 - Whisk together flour, baking powder, cinnamon, nutmeg, and salt in a medium bowl until well combined.
03 - Beat softened butter and granulated sugar in a large bowl until light and fluffy, approximately 3-4 minutes. Add eggs one at a time, mixing thoroughly after each addition, then stir in vanilla extract.
04 - Alternate adding flour mixture and milk to the butter mixture, beginning and ending with flour. Mix until just combined, being careful not to overmix.
05 - Gently fold sliced apples into the batter. Spread evenly into the prepared pan, smoothing the top with a spatula.
06 - Mix 2 tablespoons sugar with ½ teaspoon cinnamon and sprinkle evenly over the cake batter.
07 - Bake for 50-55 minutes until a toothpick inserted in the center comes out clean. Cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.
08 - While cake cools, heat milk in a saucepan until just simmering, watching carefully to prevent boiling over.
09 - Whisk egg yolks, sugar, and cornstarch in a bowl until smooth and pale in color.
10 - Gradually whisk hot milk into the yolk mixture, then return everything to the saucepan.
11 - Cook over medium-low heat, stirring constantly, until custard thickens and coats the back of a spoon, about 5 minutes. Remove from heat immediately to prevent curdling.
12 - Stir in vanilla extract until fully incorporated. Keep warm until serving.
13 - Slice cake and serve warm or at room temperature, pouring warm vanilla custard generously over each portion.