01 - Preheat the oven to 350°F. Grease and line an 8-inch round cake pan with parchment paper.
02 - In a large bowl, whisk together the flour, baking powder, salt, cinnamon, and nutmeg.
03 - Add the chilled butter and rub it into the flour mixture with your fingertips until it resembles coarse crumbs.
04 - Stir in the sugar, then fold in the sliced apples to coat them well.
05 - In a separate bowl, whisk together the eggs, milk, and vanilla extract. Pour over the apple mixture and gently mix until just combined.
06 - Transfer the batter to the prepared pan and smooth the top.
07 - Bake for 50–55 minutes, or until a skewer inserted into the center comes out clean and the top is golden brown.
08 - Cool in the pan for 10 minutes, then transfer to a wire rack.
09 - While the cake bakes, prepare the custard: In a saucepan, heat the milk over medium heat until just simmering.
10 - In a bowl, whisk together egg yolks, sugar, and cornstarch until smooth.
11 - Slowly pour the hot milk into the egg mixture, whisking constantly. Return the mixture to the saucepan.
12 - Cook over low heat, stirring constantly, until the custard thickens enough to coat the back of a spoon (do not boil).
13 - Remove from heat and stir in vanilla extract.
14 - To serve, slice the apple cake and pour warm custard over each piece.