01 - Preheat oven to 350°F. Grease and line an 8-inch round cake pan with parchment paper.
02 - Whisk together flour, baking powder, salt, cinnamon, and nutmeg in a large bowl.
03 - Add chilled butter and rub into flour mixture with fingertips until mixture resembles coarse crumbs.
04 - Stir in sugar, then fold in sliced apples until well coated.
05 - Whisk together eggs, milk, and vanilla extract in a separate bowl.
06 - Pour egg mixture over apple mixture. Gently fold until just combined.
07 - Transfer batter to prepared pan and smooth top. Bake for 50-55 minutes until skewer inserted in center comes out clean and top is golden brown.
08 - Cool in pan for 10 minutes, then transfer to wire rack.
09 - Heat milk in saucepan over medium heat until just simmering.
10 - Whisk together egg yolks, sugar, and cornstarch until smooth.
11 - Slowly pour hot milk into egg mixture while whisking constantly. Return mixture to saucepan.
12 - Cook over low heat, stirring constantly, until custard thickens enough to coat back of spoon. Do not boil.
13 - Remove from heat and stir in vanilla extract.
14 - Slice apple cake and pour warm custard over each portion.