Set a rack on the lowest level of the oven and preheat to 350°F. Roll out dough on a well-floured surface and transfer to a 9″ pie dish, crimping the edges as desired with fingers or a fork.
To make the filling, place apples in a large sauté pan with butter and sugar. Cook over high heat, stirring and tossing, for 5-7 minutes until about half of the apples have dissolved. Transfer the apple mixture to a bowl to cool.
To make the custard, whisk together the flour and sugar in a bowl, then whisk in the eggs, vanilla, and sour cream in that order.
To make the topping, mix the flour, sugar, baking powder, and cinnamon together in a bowl. Pour in the melted butter and stir until the mixture forms a crumbly mass.
Stir the cooked apples into the sour-cream custard filling and pour into the dough-lined pan. Sprinkle the crumbs over the filling.
Bake the pie until the dough is baked through, the filling is set, and the crumbs are a deep golden color, 50-60 minutes.
Cool the pie on a rack.