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 until thoroughly combined.
03 - Rub cold, cubed butter into the dry mixture using fingertips until the texture resembles coarse crumbs.
04 - Add sliced apples to the flour mixture and toss until evenly coated.
05 - Whisk eggs, milk, and vanilla extract in a separate bowl until smooth.
06 - Pour the egg mixture over the apple mixture. Fold gently until just combined, being careful not to overmix.
07 - Transfer batter to the prepared pan and spread evenly. Sprinkle turbinado or demerara sugar across the surface.
08 - Bake for 45-50 minutes until a skewer inserted into the center comes out clean and the top is golden brown. Cool in the pan for 15 minutes, then transfer to a wire rack.
09 - While the cake bakes, heat milk in a medium saucepan over medium heat until just steaming. Do not boil.
10 - Whisk egg yolks, sugar, and cornstarch in a bowl until completely smooth.
11 - Gradually whisk the hot milk into the egg mixture, pouring slowly to prevent curdling.
12 - Return the mixture to the saucepan and cook over low heat, stirring constantly, for 5-7 minutes until thickened enough to coat the back of a spoon. Remove from heat and stir in vanilla extract.
13 - Serve warm cake slices with a generous pour of custard.