Prepare the custard: Warm the milk until steaming. Whisk egg yolks and sugar, slowly add the hot milk, then return the mixture to the saucepan. Cook gently, stirring, until it coats the back of a spoon. Stir in vanilla, strain, cover the surface, and chill.
Prepare the pan: Heat the oven to 175°C and grease a 23 cm springform pan.
Make the batter: Beat softened butter and granulated sugar until fluffy. Add eggs one at a time, then mix in milk. Fold in flour, baking powder, cinnamon, and salt.
Layer the cake: Spread batter into the pan and cover evenly with thinly sliced apples.
Add the streusel: Rub cold butter into flour, oats, and brown sugar until crumbly. Scatter over the apples.
Bake: Bake for 50 to 60 minutes, until golden and set in the center. Cool for 15 minutes before removing from the pan.
Serve: Dust with powdered sugar and serve warm or at room temperature with custard sauce.