Preheat the oven to 350 F, and position a rack in the center of the oven. Spray an 8 or 9 inch springform pan with a removable bottom with non-stick baking spray.
In a saucepan, melt the butter over medium heat. Continue to cook the butter until nutty, golden brown milk solids form at the bottom of the pan. This process might take about 10 minutes. First the butter will hiss and splatter as the water evaporates, then as it quiets down, a layer of foam will form on top of the butter. This means the butter is done. Immediately remove from the heat, and scrape the butter, including the brown milk solids, into a large bowl. Let cool for 10 minutes.
In a bowl, whisk together the cooled brown butter with the granulated sugar, eggs, vanilla extract, milk and sour cream, until combined.
In a separate bowl, sift together the flour, salt, baking powder, cardamom and cinnamon. Add the almond flour, then whisk until everything is evenly distributed.
Add the dry ingredients to the wet, whisking just until moistened, then spread the batter into the prepared pan.
Peel and core the apples. You can thinly slice the apples like I did, or cut them into thicker slices, or even chunks. Arrange the apples over the cake batter any way that you like, then sprinkle the apples with 2 tbsp of the cinnamon sugar.
Bake the cake for about 80-90 minutes (for an 8 inch pan), until a cake tester inserted in the center of the cake comes out clean, or with moist crumbs clinging to it. It seems like a very long bake time, but with the moist apples on top of the batter, the cake does take this long to bake through in the middle.Baker's Note: I used an 8-inch pan and my cake was done at 85 minutes. If you use a 9-inch pan, you'll likely need to bake your cake for 10-15 minutes less. Set the pan on a cooling rack and let the cake cool for 1 1/2 - 2 hours. Loosen and remove the collar from the pan, and serve the cake warm, or at room temperature. Before serving, sprinkle the top of the cake with the remaining 1 tbsp of cinnamon sugar.
Store leftover cake in an airtight container at room temperature for up to 2 days, or in the refrigerator for up to 4-5 days.