01 - Preheat the oven to 350°F. Grease a 9-inch round cake pan and line with parchment paper.
02 - Sift together flour, baking powder, cinnamon, nutmeg, and salt in a large bowl.
03 - Rub cold diced butter into the flour mixture with your fingertips until it resembles coarse breadcrumbs.
04 - Stir granulated sugar into the butter-flour mixture until evenly distributed.
05 - Whisk eggs, milk, and vanilla extract in a separate bowl until combined.
06 - Pour the egg mixture into the flour mixture and mix until just combined.
07 - Gently fold sliced apples into the batter, ensuring even distribution throughout.
08 - Spread batter evenly in the prepared pan. Bake for 45 to 50 minutes until golden brown and a skewer inserted in the center comes out clean.
09 - Let the cake cool in the pan for 10 minutes, then transfer to a wire rack.
10 - Heat milk in a saucepan over medium heat until just simmering, being careful not to boil.
11 - Whisk egg yolks, sugar, and cornstarch in a bowl until pale and thickened.
12 - Gradually pour hot milk into the yolk mixture while whisking constantly to prevent curdling.
13 - Return mixture to the saucepan and cook over low heat, stirring constantly, until thickened enough to coat the back of a spoon, about 3 to 5 minutes.
14 - Remove from heat and stir in vanilla extract.
15 - Serve cake warm or at room temperature with warm custard poured over each slice.