01 - Preheat the oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - In a large bowl, whisk together flour, baking powder, cinnamon, nutmeg, and salt.
03 - Cut the cold butter into the flour mixture using a pastry blender or fingertips until it resembles coarse crumbs.
04 - Stir in the sugar, then fold in the sliced apples to coat evenly.
05 - In a separate bowl, whisk together eggs, milk, and vanilla extract. Pour into the apple-flour mixture and gently mix until just combined, being careful not to overmix.
06 - Spoon the batter into the prepared pan and smooth the top.
07 - Bake for 45 to 50 minutes, or until golden and a skewer inserted into the center comes out clean. Cool in the pan for 10 minutes, then transfer to a wire rack.
08 - While the cake bakes, heat milk in a saucepan until just steaming, being careful not to boil.
09 - In a bowl, whisk egg yolks, sugar, and cornstarch until pale. Gradually whisk in the hot milk.
10 - Return the mixture to the saucepan and cook over low heat, stirring constantly, until thickened and it coats the back of a spoon, approximately 5 to 7 minutes. Remove from heat and stir in vanilla extract.
11 - Serve the apple cake warm or at room temperature with warm custard sauce drizzled over each slice.