Place the milk and peanut butter in a medium saucepan. Heat over medium-low, stirring occasionally, until mixture just begins to simmer and peanut butter has melted completely.

While the peanut butter mixture is heating, whisk together the sugar, salt and egg yolks in a medium bowl. Gradually pour the peanut butter mixture into the egg yolks; whisking vigorously the entire time.

Return the mixture to the saucepan and cook over medium-low heat, stirring constantly, until the mixture thickens noticeably and coats a wooden spoon. (~4-6 minutes)

Remove mixture from heat and add the heavy cream; stir until well combined.

Pour/gently press the mixture through a fine-mesh strainer into a clean container. Stir in the vanilla extract. Cover with plastic wrap, pressing the plastic directly onto the surface of the mixture, and refrigerate overnight.

Pour the ice cream mixture into an ice cream maker and freeze according to the manufacturer's directions.

Meanwhile, melt the peanut butter for the swirl in either a small saucepan or the microwave. Set melted peanut butter aside to cool slightly.

Once churned, transfer ice cream into a freezer-safe container. Drop spoonfuls of melted peanut butter into container and swirl together using a butter knife. Serve immediately (softer ice cream) or transfer into the freezer for a couple of hours (harder ice cream).