01 - Preheat 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 cold butter into the flour mixture using a pastry blender or fingertips until mixture resembles coarse crumbs.
04 - Stir in sugar, then fold in sliced apples to coat evenly.
05 - In a separate bowl, whisk together eggs, milk, and vanilla extract. Pour into apple-flour mixture and gently mix until just combined without overmixing.
06 - Spoon batter into prepared pan and smooth the top surface.
07 - Bake for 45 to 50 minutes until golden brown and a skewer inserted into the center comes out clean. Cool in pan for 10 minutes, then transfer to wire rack.
08 - While cake bakes, heat 2 cups milk in a saucepan until just steaming, without boiling.
09 - In a bowl, whisk egg yolks, sugar, and cornstarch until pale. Gradually whisk in hot milk.
10 - Return mixture to saucepan and cook over low heat, stirring constantly, until thickened and coats the back of a spoon, approximately 5 to 7 minutes. Remove from heat and stir in vanilla.
11 - Serve apple cake warm or at room temperature with warm custard sauce drizzled over each slice.