Preheat oven to 350 degrees F (175 degrees C).

In a medium bowl, stir together the melted butter, sugar, egg, and cake flour until the mixture starts to hang together, then use your hands to bring it into a soft dough. Press a bit more than half of the dough evenly over the bottom and up the sides of a 9-inch pie dish, building the edge up slightly to help hold in the filling.

Fill the crust with the sliced apples and sprinkle them evenly with the ground cinnamon. Crumble the remaining dough over the top of the apples until they're mostly covered (a few visible gaps are fine). For a sugary top crust, sprinkle a handful of sugar over the crumbles. Bake in the preheated oven for 45 minutes, or until the topping is golden brown and the filling is bubbling around the edges.

Remove the pie from the oven and let it cool for at least 30 minutes on a cooling rack before slicing, so the filling has time to set. Slice and serve.