Step 1: In a medium saucepan, combine the whole milk, heavy cream, granulated sugar, and brown sugar. Heat over medium heat, stirring occasionally, until the mixture is hot and small bubbles form around the edges.
Step 2: While the dairy is heating, whisk the egg yolks in a separate heat-proof bowl until they are pale and slightly thickened.
Step 3: Slowly pour about 1/2 cup of the hot milk mixture into the egg yolks in a thin stream, whisking constantly to temper the eggs without scrambling them.
Step 4: Pour the tempered egg mixture back into the saucepan with the remaining milk. Cook over medium-low heat, stirring constantly with a wooden spoon or spatula, until the custard thickens enough to coat the back of the spoon.
Step 5: Remove the saucepan from the heat and whisk in the pumpkin puree, vanilla extract, cinnamon, ginger, cloves, nutmeg, and salt until completely smooth.
Step 6: Strain the mixture through a fine-mesh sieve into a clean bowl to remove any lumps. Cover the surface directly with plastic wrap and refrigerate for at least 6 hours, or overnight.
Step 7: Pour the chilled custard into your ice cream maker and churn according to the manufacturer’s instructions (usually 20-25 minutes).
Step 8: In the last 2 minutes of churning, add the crushed graham crackers if using. Transfer to a container and freeze for at least 4 hours to firm up before serving.