01 - Preheat the oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - In a large bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt.
03 - Add the cold, cubed butter and rub it into the flour mixture with your fingertips until it resembles coarse breadcrumbs.
04 - Stir in the granulated sugar. Add the sliced apples and toss to coat evenly.
05 - In a separate bowl, whisk together the eggs, milk, and vanilla extract.
06 - Pour the wet ingredients into the dry mixture and stir gently until just combined. Do not overmix.
07 - Transfer the batter to the prepared cake pan, spreading it evenly. Sprinkle the top with demerara or turbinado sugar. Bake for 45 minutes, or until golden and a toothpick inserted in the center comes out clean. Allow to cool for 10 minutes before removing from the pan.
08 - While the cake bakes, prepare the custard. In a saucepan, heat the milk over medium heat until just steaming.
09 - In a bowl, whisk together the egg yolks, sugar, and cornstarch until pale and smooth.
10 - Gradually pour the hot milk into the egg mixture, whisking constantly.
11 - Return the mixture to the saucepan and cook over low heat, stirring constantly, until thickened, about 5 minutes. Do not let it boil. Remove from heat and stir in the vanilla extract.
12 - Serve the apple cake warm or at room temperature, drizzled with the warm custard.