01 - Preheat the oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - Sift together flour, baking powder, cinnamon, nutmeg, and salt in a large bowl.
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 - Whisk together eggs, milk, and vanilla extract in a separate bowl.
06 - Pour the wet ingredients into the flour mixture and mix until just combined.
07 - Gently fold in the apple slices, ensuring they are well distributed throughout the batter.
08 - Spoon the batter into the prepared pan and spread evenly.
09 - 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.
10 - Heat milk in a saucepan over medium heat until just simmering. Do not boil.
11 - Whisk egg yolks, sugar, and cornstarch until pale and thick.
12 - Gradually pour the hot milk into the yolk mixture, whisking constantly to prevent curdling.
13 - 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.
14 - Remove from heat and stir in vanilla extract.
15 - Serve the apple cake warm or at room temperature, with the custard poured over each slice.