If you have whole cardamom pods, please see these instructions for crushing them. Crush the pods in a mortar and pestle or in between waxed paper. Discard the pod shells. Crush the tiny black seeds slightly to make them more aromatic. Heat the milk and the cream with the crushed cardamom and half of the sugar until very hot, but not boiling.
In a medium-sized bowl, whisk together the egg yolks and the remaining half of the sugar.
When the milk is hot, temper the eggs by whisking in a cup of the hot milk and cream into the bowl with the eggs and sugar. This keeps the eggs from scrambling when you add them to the hot milk. Then whisk the egg/milk mixture back into the pot with the hot cream. Cook until the custard begins to thicken; do not boil or the eggs may cook and curdle.
Pour the custard through a fine-mesh strainer and chill until very cold. At least 3 hours or overnight.
Whisk in the vanilla extract and then stir in the persimmon pulp. Freeze in your ice cream maker according to the manufacturer's directions. I use the Cuisinart Ice Cream Maker.