Preheat oven to 350 degrees. Invert the bottom of an 8" springform pan (to make it easier to slide the cake off the bottom) then lock on the sides of the pan. Lightly grease and flour the bottom and sides of the pan. Line the bottom with a round of parchment paper and set aside.
Sift together the flour, salt, baking powder and cinnamon. Set aside.
Peel, core and thinly slice the apples and place them in a large mixing bowl. Toss the apples with 3 tablespoons of flour and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar. Beat for several minutes until light and fluffy. Scrape down the sides of the bowl as needed.
Beat in the eggs, one at a time, just until the yolk disappears. And the vanilla bean paste and mix just until blended.
Add 1/3 of the flour mixture to the creamed butter and sugar. Beat on low until incorporated. Add about 1/2 of the milk and blend until smooth. Repeat adding 1/2 of the remaining flour, then all the remaining milk. Finally, blend in the last of the flour mixture and mix just until incorporated. Scrape up the batter from the bottom of the bowl give it one last spin. Fold in the apples.
Pour the batter into the prepared pan and spread evenly. Sprinkle with the crumble topping (leaving some in large clumps). Place a large sheet of foil on the lower oven rack to catch any drips that may come from the cake. Bake in the preheated oven for 50-60 minutes or until the top is lightly browned and a toothpick inserted in the center comes out almost clean. Cover the cake with foil during the last 15 minutes of baking if needed to prevent over browning. Check the cake by inserting a toothpick in the center. It should come out with only crumbs attached, no wet batter.
Cool the cake on a wire rack for at least 30 minutes if serving warm, or cool completely before removing the sides. Carefully slide the cake onto a serving platter and dust with powdered sugar before serving.
Top with a Apple Brandy Sauce if desired. Refrigerate leftovers.