Combine cream, milk, 1/4 cup of the granulated sugar, and brown sugar in a medium saucepan over medium heat. Heat just until bubbles start to form around the edges of the pan.

Meanwhile, combine the remaining 1/4 cup of granulated sugar, egg yolks, pumpkin puree, cinnamon, ginger, nutmeg, allspice, and salt in a medium bowl and whisk well.

When the milk/cream mixture is hot, pour 1/2 cup into the egg mixture, whisking well to temper the egg yolks so they don't scramble. Add another half cup of the hot liquid and whisk again. Pour the tempered egg yolk mixture into the saucepan with the remaining cream mixture and heat until the custard base reaches 160 to 170 degrees F. Remove from the heat and stir in the vanilla.

Cool completely and chill in the fridge or in a sealed, reusable silicon bag set into an ice bath until completely cold before churning.

Once the mixture is thoroughly chilled, pour it into your ice cream maker and churn for 20-30 minutes until the consistency of soft serve. Transfer to a freezer safe container like a bread pan and freeze for 4 hours until firm.