01 - Preheat oven to 350°F. Grease a 9-inch round cake pan with butter and line the base with parchment paper.
02 - Sift flour, baking powder, cinnamon, nutmeg, and salt into a large mixing bowl.
03 - Add cold cubed butter to the flour mixture. Rub with fingertips until texture resembles coarse breadcrumbs.
04 - Stir in granulated sugar, then fold in sliced apples until evenly coated with the flour mixture.
05 - Whisk eggs, milk, and vanilla extract in a separate bowl until fully blended.
06 - Pour wet ingredients into dry mixture. Mix gently until just combined—do not overmix.
07 - Spread batter evenly into prepared pan. Bake for 50-55 minutes until golden brown and a skewer inserted into center comes out clean. Cool in pan for 10 minutes, then transfer to wire rack.
08 - Warm milk in saucepan until just steaming—do not allow to boil.
09 - Whisk egg yolks, sugar, and cornstarch in a bowl until smooth and pale.
10 - Gradually pour hot milk into egg mixture while whisking constantly. Return mixture to saucepan. Cook over low heat, stirring continuously, until thickened and coating the back of a spoon. Remove from heat and stir in vanilla extract.
11 - Serve cake warm or at room temperature with warm custard poured over individual slices.