Preheat oven to 350F. and grease an 8-inch springform pan. *A parchment round on the bottom of the pan is recommended if you plan on removing the cake to a serving platter. Set the springform pan on a baking sheet and set aside. *Note: if you are using a dark springform pan, reduce temperature to 340F.
Make the cake: In a food processor, add the flour, sugar and baking powder. Pulse a couple of times to combine. Add the cold butter and pulse until the butter is combined with the flour. You'll end up with a very dry mixture, like sand almost.
Sprinkle about 3/4 of this mixture over the bottom of the prepared springform pan. Don't press it down at all, but move it around a bit so it goes up the sides just a bit. Scatter the prepared apple slices over the crumbs (avoiding the sides), then sprinkle the remaining crumb mixture evenly over the top. Again, do not press down. Leave it as is. Place the springform pan on top of a baking sheet (to catch any liquid from the apples that might leak from the pan!). Bake in the preheated oven for 20 minutes.
Meanwhile, in a medium bowl, whisk together the eggs, cream, sour cream, brown sugar, vanilla and a pinch of salt. Set aside.
When cake base has baked 20 minutes, remove from oven and carefully pour the egg mixture over the top. REDUCE THE OVEN TEMPERATURE TO 325F (or 315F for a dark pan and return the cake to oven and cook for a further 20 minutes.
Meanwhile, prepare the crumble topping. In a small bowl, combine the flour, sugar, cinnamon and a pinch of salt. Add melted butter to the mixture, just until the dry ingredients are moistened and the mixture comes together in large clumps. Place the bowl into the freezer until needed.
When the cake has baked for 20 minutes, remove from oven. (The egg mixture should have set somewhat so that the crumbs won't sink into the cake. If it is quite liquid still, return to the oven for a few more minutes.) Evenly sprinkle the crumb mixture over the top. Return to the oven and bake a further 20 - 30 minutes or until the edges are pulled away from the sides of the pan, the top crumbles are light golden and the centre is set. As long as it's not too jiggly and a tester inserted in the centre comes out with just crumbs (not liquid), it's ready to take out of the oven. It should have bake about 60-65 total, including all 3 steps.
Allow to cool in the pan, on a cooling rack, for 10 minutes. Run a knife around the outside and carefully remove the outer ring of the springform pan. Allow to cool more before removing from the base.
Dust with powdered/icing sugar, if desired.
Be sure to read the Ingredient and Cook's Notes above this recipe card, for more tips on making this recipe. You will also find Step-by-Step photos of the process of making this cake.