Preheat oven to 350°. Spray the sides of a 9¾x2-inch enameled cast-iron tarte Tatin dish with baking spray with flour.*
Pour melted butter into bottom of prepared dish. Evenly sprinkle with brown sugar. Place 1 persimmon slice in center of the dish over the brown sugar. Cut remaining persimmon slices in half. Working from the center out, arrange persimmon slices in a single layer in 2 concentric circles, overlapping slices and changing directions to the opposite way for the second circle. Use any remaining slices to cover any holes, if desired.
In the bowl of a stand mixer fitted with the paddle attachment, beat softened butter and granulated sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in zest and vanilla.
In a medium bowl, whisk together flour, baking powder, salt, baking soda, nutmeg, and cloves. With mixer on low speed, gradually add flour mixture to butter mixture alternately with buttermilk, beginning and ending with flour mixture, beating just until combined after each addition. Fold in ginger. Pour batter over persimmons, smoothing with an of set spatula (dish will be full but will not overflow in oven).
Bake until a wooden pick inserted in center comes out clean, 45 to 50 minutes. Let cool in pan for 5 to 10 minutes. Run a knife around edges of pan to release sides of cake; carefully invert onto parchment paper on a flat serving plate. Let cool 30 minutes. Serve warm or at room temperature.
Notes
*If you do not have a tarte Tatin dish, use a 10-inch cast-iron skillet.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/persimmon-ginger-upside-down-cake-recipe/