In a large, heavy-bottomed saucepan, combine the heavy cream, whole milk, granulated sugar, and salt. Heat over medium heat, stirring occasionally, until the mixture is hot and steaming, but not boiling. Remove from heat just as it starts to simmer.

In a separate medium bowl, whisk the egg yolks until light yellow and slightly thickened. Slowly pour about half of the hot cream mixture into the whisked egg yolks, whisking constantly to temper them and prevent scrambling. This step is crucial for a smooth custard.

Pour the tempered egg yolk mixture back into the saucepan with the remaining cream mixture. Return the saucepan to medium-low heat and cook, stirring constantly with a wooden spoon or spatula, until the custard thickens enough to coat the back of the spoon (reaching about 175-180°F or 80-82°C). Do not allow the mixture to boil, as this will curdle the eggs.

Remove the saucepan from the heat. Stir in the creamy peanut butter and honey until completely melted and smooth. Add the vanilla extract and stir to combine thoroughly.

Strain the custard through a fine-mesh sieve into a clean large bowl to remove any potential bits of cooked egg or undissolved solids. Set the bowl over a larger bowl filled with ice and water (an ice bath). Stir occasionally until the mixture cools down significantly. Once cooled, cover the bowl tightly with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled. This chilling step is vital for the best ice cream texture.

Once the base is thoroughly chilled, pour it into your ice cream maker and churn according to the manufacturer's instructions. This typically takes 25-35 minutes, resulting in a soft-serve consistency.

Transfer the freshly churned ice cream to an airtight freezer-safe container. Press a piece of parchment paper directly onto the surface of the ice cream to prevent ice crystals from forming, then secure with a lid. Freeze for at least 4-6 hours, or until firm, before serving.