Method

Prepare the topping

1. Coat a 9-inch cake pan with baking spray. Line the bottom with parchment paper. Lightly spray the paper with baking spray. 
2. Place the butter in a small bowl and melt it in the microwave. Immediately stir in the brown sugar and salt. Mix well to combine. 
3. Pour the brown sugar mixture into the prepared pan, and spread it with an offset spatula to cover the bottom of the pan completely.
4. Starting from the outside of the pan, layer the persimmon slices, with the straight side lying inwards, slightly overlapping them in concentric circles until you reach the center. Leave no gaps.

Prepare the cake

1. In a medium bowl, add the all-purpose flour, almond flour, baking powder, baking soda, salt, ground ginger and ground cardamom, and mix well until well combined.
2. In a small saucepan, on medium to low heat, add the butter. As the butter starts melting, make sure to stir it occasionally to ensure that it melts evenly. You want to brown the butter here, which takes about 6 to 7 minutes total. First you will start seeing foam and then bubbles. As soon as you whiff a nutty fragrance, the butter has started browning. It happens quickly, with the milk solids at the bottom looking toasty and dark brown. Remove from the heat immediately and pour butter into a bowl to stop the browning. Let cool.
3. Preheat the oven to 350 degrees.
4. Pour the browned butter into a large bowl. Add the granulated sugar and mix with a rubber spatula. Add the yogurt and oil and mix to combine. Add the eggs, one at a time, and mix well to combine. Add the persimmon puree and vanilla and stir to combine. Add the orange zest and mix again.
5. Add the dry ingredients and the walnuts to the wet ingredients, stirring until just combined. Do not overmix.
6. Pour the cake batter on top of the arranged persimmon slices, and spread evenly using an offset spatula.
7. Place the cake pan in the lower middle rack of the oven. Bake for about 35 to 40 minutes, until golden brown on the top and a cake tester inserted into the center comes out clean. Allow the cake to cool for about 30 minutes.
8. Place an offset spatula between the pan and the cake and run it vertically around the pan to release the cake from the sides.
9. Place a plate on top of the cake pan, and gently invert it.
10. Gently remove the parchment paper from the top to reveal the persimmons.
11. Let cool completely for another 30 minutes.

Dried persimmon flowers

1. Preheat the oven to 180 degrees. Place the persimmon slices onto a wire rack, placed on a baking sheet, and place the sheet in the oven for about 2 to 2½ hours. As the moisture  evaporates,  the slices will shrivel and look like flowers. 
2. Store in an airtight container for up to 2 weeks.

To serve:  Serve the cake with the whipped cream and persimmon flowers. The cake will keep in a cool place for up to 3 days. Keep it covered to prevent drying.

Notes:

1. The persimmon puree should be from the Hachiya persimmon variety. Ripen them faster by placing them in a brown paper bag, along with an apple. The persimmons should ripen within 3 to 4 days. Peel the skin off and blend the pulp.
2. You can also use an 8×8 cake pan if you do not have a 9×9 cake pan. Check for doneness with the cake tester inserted in the center of the cake, after 35 to 40 minutes, and ensure that it comes out clean.