1. Mix the half-and-half and sugar together in a heavy saucepan.
2. Add the ginger, cinnamon, cloves, and allspice.
3. Place the saucepan over medium heat and stir until the sugar dissolves.
4. Remove the saucepan from the heat, cover, and let steep for 45 minutes.
5. Pour the mixture through a wire mesh strainer to remove the ginger and spices.
6. Clean the strainer and set it aside close at hand, with a clean bowl.
7. Pour the cream mixture back into the saucepan and reheat it over a medium flame until very hot to the touch.
8. Whisk the egg yolks together in a spacious, heat-tolerant bowl. Temper the yolks by slowly adding one cup of the hot cream mixture while whisking vigorously.
9. Reduce the heat to medium-low and whisk the tempered yolks into the saucepan, creating custard. Stir constantly until the custard thickens slightly and coats the back of a wooden spoon. Immediately remove from the heat and strain it into a clean bowl.
10. Allow the custard to cool to room temperature (approximately one hour).
11. Add the persimmon puree and vanilla. Mix well.
12. Strain the mixture once again, cover with plastic wrap, and refrigerate for 4–6 hours, or overnight.
13. Place the cold custard in the canister of your ice cream maker and process according to the manufacturer’s instructions.
14. Transfer the ice cream to a container, cover, and freeze 8 hours or overnight to firm up.

NOTE: For best flavor, always remove ice cream from the freezer 20 minutes before serving, or place it in the microwave for 20 seconds.