In a large bowl, whisk eggs until light and fluffy, 1 to 2 minutes. Whisk in sugar, a little at a time, then continue whisking until completely blended, about 1 minute. Pour in cream and milk, whisk to blend.
Pour 1 cup of cream base into another bowl and add pumpkin, nutmeg and cinnamon and stir until blended. Return pumpkin mixture to the remaining cream base and blend. Cover with plastic wrap. Chill in freezer until very cold (40 degrees) about 30 to 60 minutes.
Start ice cream maker and add the mixture. Mix until ice cream has the consistency of soft serve ice cream, about 25 to 30 minutes. In the last 2 minutes of mixing, add the gingersnaps.
Remove from ice cream machine canister and transfer to an airtight container. Freeze until firm, at least 3 hours.