01 - Preheat oven to 350°F. Grease an 8-inch round cake pan and line with parchment paper.
02 - Whisk together flour, baking powder, cinnamon, nutmeg, and salt in a large bowl.
03 - Rub cold butter into flour mixture with fingertips until mixture resembles coarse crumbs.
04 - Stir granulated sugar into the butter-flour mixture until evenly distributed.
05 - Whisk eggs, milk, and vanilla extract in a separate bowl until well blended.
06 - Pour wet ingredients into dry mixture. Stir until just combined, taking care not to overmix.
07 - Gently fold sliced apples into batter until evenly distributed throughout.
08 - Transfer batter to prepared pan, smooth top surface, and sprinkle with demerara sugar.
09 - Bake for 45 to 50 minutes until a skewer inserted into center comes out clean and top is golden brown.
10 - Let cake rest in pan for 10 minutes, then transfer to wire rack to cool further.
11 - Heat milk in saucepan over medium heat until just simmering, being careful not to boil.
12 - Whisk egg yolks, sugar, cornstarch, vanilla, and salt in a bowl until smooth.
13 - Slowly pour hot milk into egg mixture while whisking constantly to prevent curdling.
14 - Return mixture to saucepan and cook over low heat, stirring constantly until thickened enough to coat a spoon, about 5 to 7 minutes. Do not boil.
15 - Remove custard from heat and serve warm alongside slices of apple cake.