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