01 - Preheat oven to 350°F. Grease a 9-inch round cake pan and line the base with parchment paper.
02 - In a large bowl, sift together flour, baking powder, cinnamon, nutmeg, and salt.
03 - Add the cold butter and rub into the flour mixture with your fingertips until it resembles coarse breadcrumbs.
04 - Stir in the sugar and then fold in the sliced apples until evenly coated.
05 - In a separate bowl, whisk eggs, milk, and vanilla extract. Pour into the dry ingredients and mix until just combined.
06 - Spread the batter into the prepared pan, smoothing the top. Bake for 50–55 minutes, or until golden brown and a skewer inserted into the center comes out clean. Cool in the pan for 10 minutes, then transfer to a wire rack.
07 - In a saucepan, heat milk until just steaming, being careful not to boil.
08 - In a bowl, whisk egg yolks, sugar, and cornstarch until smooth.
09 - Gradually pour the hot milk into the egg mixture, whisking constantly. Return the mixture to the saucepan and cook over low heat, stirring continuously, until thickened and coats the back of a spoon. Do not let it boil.
10 - Remove from heat and stir in vanilla extract. Serve the cake warm or at room temperature with the warm custard poured over.