Mix egg yolks and sugar in a large bowl.
Heat milk with the vanilla pod and seeds in a saucepan until just boiling.
Remove from heat, cool for one minute, and remove the vanilla pod.
Whisk the warm milk into the yolk mixture vigorously.
Heat the mixture in a pan, stirring continuously until it coats a spoon.
Toss chopped apple with cinnamon and brown sugar in a bowl.
Place portions of the apple mixture onto the centers of the pastry squares.
Brush edges with beaten egg and fold pastry over to create triangles.
Brush the exterior of the triangles with egg wash.
Heat vegetable oil in a heavy-bottomed saucepan until hot.
Fry the strudels until golden brown, then drain on towels and dust with icing sugar.
Serve the strudels drizzled with the prepared custard.