1Prepare an ice water bath by filling a bowl halfway with ice and water; set it aside. Place a fine-mesh strainer over a large heatproof bowl; set it aside.
2Whisk together the cream, 1/2 cup of the brown sugar, the pumpkin, milk, salt, and vanilla in a medium saucepan until smooth. Heat the mixture over medium heat, whisking occasionally, until steam begins to rise from the surface, about 5 minutes. Meanwhile, whisk the remaining 1/2 cup of sugar, egg yolks, cinnamon, and ginger in a large bowl until smooth; set aside.
3While whisking constantly, slowly pour about half of the heated cream mixture into the egg yolk mixture. Pour the cream-egg mixture back into the pan and cook over medium heat, stirring constantly with a wooden spoon or rubber spatula, until the mixture thickens slightly and coats the back of the spoon or registers 170°F on an instant-read thermometer, about 2 minutes. (Don’t let the mixture boil.) When you draw your finger across the spoon, it should make a mark through the custard, which should not run back in on itself.
4Pour the custard through the prepared strainer into the bowl and discard the contents of the strainer. Place the bowl in the ice water bath and let the custard cool, stirring occasionally, until it reaches room temperature, about 20 minutes.
5Press a sheet of plastic wrap directly onto the surface of the custard to prevent a skin from forming. Refrigerate until completely chilled, at least 4 hours.
6Churn the chilled custard in an ice cream maker according to the manufacturer’s instructions. Serve immediately for a soft ice cream, or transfer to an airtight container and freeze until solid. Allow the ice cream to sit at room temperature for 15 minutes before serving if frozen solid. The ice cream can be kept for up to 1 month.