01 - Preheat the oven to 350°F. Grease an 8-inch round cake pan and line with parchment paper.
02 - Whisk together flour, granulated sugar, baking powder, salt, cinnamon, and nutmeg in a large bowl.
03 - Rub the cold, cubed butter into the dry ingredients using your fingertips until the mixture resembles coarse crumbs.
04 - Add the sliced apples to the flour mixture and toss to coat evenly.
05 - Whisk eggs, milk, and vanilla extract together in a separate bowl.
06 - Pour the wet mixture over the apple mixture and gently fold until just combined.
07 - Transfer the batter to the prepared cake pan, spreading evenly. Sprinkle turbinado sugar over the top.
08 - Bake for 45-50 minutes until a skewer inserted into the center comes out clean and the top is golden. Cool in the pan for 15 minutes, then transfer to a wire rack.
09 - Heat the milk in a medium saucepan over medium heat until just steaming, not boiling.
10 - Whisk egg yolks, sugar, and cornstarch in a bowl until smooth.
11 - Gradually whisk the hot milk into the egg mixture, then return the mixture to the saucepan.
12 - Cook over low heat, stirring constantly, until the custard thickens and coats the back of a spoon for 5-7 minutes. Do not boil. Remove from heat and stir in vanilla extract.
13 - Serve slices of warm apple cake with a generous pour of custard.