01 - Preheat the oven to 350°F. Grease and line an 8-inch round cake pan with parchment paper.
02 - In a large bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt.
03 - Rub the cold butter into the flour mixture with your fingertips until it resembles coarse crumbs. Stir in the sugar.
04 - In a separate bowl, whisk together the eggs, milk, and vanilla extract.
05 - Add the wet ingredients to the dry mixture and stir until just combined. Gently fold in the sliced apples.
06 - Pour the batter into the prepared cake pan and smooth the top. Sprinkle with demerara or granulated sugar. Bake for 45–50 minutes, or until a skewer inserted into the center comes out clean and the top is golden brown.
07 - Allow to cool in the pan for 10 minutes, then transfer to a wire rack.
08 - In a saucepan, heat the milk over medium heat until just simmering, being careful not to let it boil.
09 - In a bowl, whisk together the egg yolks, sugar, cornstarch, vanilla, and salt until smooth.
10 - Slowly pour the hot milk into the egg mixture, whisking constantly to prevent curdling.
11 - Return the mixture to the saucepan and cook over low heat, stirring constantly, until the custard thickens enough to coat the back of a spoon, about 5–7 minutes. Do not let it boil.
12 - Remove from heat and serve warm custard alongside slices of apple cake.