01 - Preheat the oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - In a large bowl, sift together flour, baking powder, cinnamon, nutmeg, and salt.
03 - Rub in the cold diced butter with your fingertips until the mixture resembles coarse breadcrumbs.
04 - Stir the sugar into the flour-butter mixture until evenly distributed.
05 - In a separate bowl, whisk eggs, milk, and vanilla extract. Pour into the flour mixture and mix until just combined.
06 - Gently fold in the apple slices, ensuring they are well distributed throughout the batter.
07 - Spoon the batter into the prepared pan and spread evenly.
08 - Bake for 45-50 minutes, or until golden brown and a skewer inserted into the center comes out clean. Cool in the pan for 10 minutes before transferring to a wire rack.
09 - While the cake bakes, heat milk in a saucepan over medium heat until just simmering, being careful not to boil.
10 - In a bowl, whisk egg yolks, sugar, and cornstarch until pale and thick.
11 - Gradually pour the hot milk into the yolk mixture, whisking constantly to prevent curdling.
12 - Return the mixture to the saucepan and cook over low heat, stirring constantly, until the custard thickens enough to coat the back of a spoon, about 3-5 minutes. Do not let it boil.
13 - Remove from heat and stir in vanilla extract.
14 - Serve the apple cake warm or at room temperature, with the custard poured over each slice.