01 - Preheat oven to 350°F. Grease an 8-inch round cake pan and line with parchment paper.
02 - In a large bowl, whisk together flour, baking powder, salt, cinnamon, and nutmeg until well blended.
03 - Rub cold cubed butter into the flour mixture with your fingertips until coarse crumbs form.
04 - Stir in ¾ cup sugar. Whisk together eggs, milk, and vanilla in a separate bowl, then add to dry ingredients. Mix until just combined.
05 - Gently fold diced apples into the batter, being careful not to overmix.
06 - Pour batter into prepared pan, smooth top, and sprinkle with 2 tablespoons sugar. Bake for 45-50 minutes until golden and a skewer comes out clean. Cool in pan for 10 minutes, then transfer to wire rack.
07 - Heat 2 cups milk in a saucepan until just below boiling. Meanwhile, whisk egg yolks, ⅓ cup sugar, and cornstarch until smooth.
08 - Gradually pour hot milk into yolk mixture while whisking constantly. Return to saucepan and cook over low heat, stirring continuously until thickened enough to coat a spoon. Do not boil. Remove from heat and stir in vanilla.
09 - Slice warm cake and serve with generous spoonfuls of warm custard sauce.