01 - Preheat oven to 350°F. Grease an 8-inch round cake pan and line with parchment paper.
02 - Whisk together flour, baking powder, cinnamon, nutmeg, and salt in a large bowl.
03 - Rub cold butter into flour mixture with fingertips until mixture resembles coarse crumbs.
04 - Stir sugar into butter-flour mixture. Whisk eggs, milk, and vanilla separately, then add to dry ingredients. Mix until just combined.
05 - Gently fold in sliced apples. Pour batter into prepared pan, smooth top, and sprinkle with demerara sugar. Bake 45–50 minutes until golden and a skewer comes out clean.
06 - Let cake cool in pan for 10 minutes, then transfer to a wire rack.
07 - Heat milk in a saucepan over medium heat until just simmering, being careful not to boil.
08 - Whisk together egg yolks, sugar, cornstarch, vanilla, and salt until smooth.
09 - Slowly pour hot milk into egg mixture while whisking constantly. Return to saucepan and cook over low heat, stirring constantly, until thickened enough to coat a spoon, about 5–7 minutes. Do not boil.
10 - Remove custard from heat and serve warm alongside slices of apple cake.