8 tablespoons unsalted butter (1 stick), melted, plus more for coating the dish
1/4 cup brandy
Heat the oven to 350°F and arrange a rack in the middle.
With a paring knife, trim away and discard the stem from one persimmon. Using a spoon, scoop out the pulp and discard the skin. Place the pulp in the bowl of a food processor fitted with a blade attachment, being careful not to include any of the tannic skin. Repeat with the remaining persimmons. Process the pulp until smooth, about 1 minute. Measure and set aside 2 cups of puréed pulp. Discard or reserve any extra pulp for another use.
Whisk together the flour, baking powder, nutmeg, salt, baking soda, cinnamon, and orange zest in a large bowl to aerate and break up any lumps; set aside. Coat a 13-by-9-inch baking dish with butter and set aside.
In the bowl of a stand mixer fitted with a whisk attachment, combine the persimmon pulp, milk, brown sugar, and eggs on low speed until evenly blended. Add the melted butter and brandy and whisk until just incorporated. Add the flour mixture in four parts, letting the flour incorporate before adding the next part and scraping down the sides of the bowl as necessary until the flour is totally incorporated.
Turn the batter into the prepared dish and bake until a cake tester inserted into the center comes out clean, about 40 minutes. Serve warm or at room temperature with toasted hazelnuts and ice cream, yogurt, or whipped cream.