Preheat oven to 350°F (175°C) and grease a 9-inch springform pan.
Prepare the custard sauce: Simmer milk, whisk egg yolks with sugar, gradually combine, and cook until thickened. Strain, add vanilla, and chill.
Make streusel topping: Mix butter, flour, sugar, and oats until crumbly, then refrigerate.
Cream butter and sugar, then beat in eggs one at a time.
Whisk together flour, baking powder, cinnamon, and salt; fold into the batter with milk or cream.
Spread batter in the prepared pan, layer with sliced apples, and sprinkle with streusel.
Bake for 50–60 minutes, until golden and set.
Cool slightly, dust with confectioner’s sugar, and serve with chilled custard sauce.