In a 2-quart, heavy-bottomed sauce pan, whisk 1 cup of the heavy cream with the cocoa powder and espresso.
Heat over medium heat until it just starts to boil, whisking frequently, then cook for an additional 30 seconds, whisking constantly.
Remove from heat and add the chocolate chips and the rest of the heavy cream and stir until smooth, then transfer to a 2-quart mixing bowl, scraping the sides well. Place a strainer over the top and set aside.
In the same sauce pan, combine the milk, sugar, and sea salt. Stirring often, heat until warm.
In a medium mixing bowl, whisk the egg yolks.
Add a few spoonfuls of the warmed milk mixture to the egg yolks, mixing constantly (this is tempering the eggs to prevent them from becoming scrambled).
Pour the egg mixture into the rest of the warmed milk, stirring constantly. Cook until thickened to the point that it coats the back of a spoon.
Pour the custard through the strainer into the chocolate mixture (so as to remove any eggs that did maybe accidentally become a little scrambled... it happens). Add the vanilla extract.
Stir until well incorporated and smooth.
Cover and refrigerate for at least 2 hours, and up to 12 hours.
Freeze in an ice cream machine per manufacturer's instructions.
Transfer to an airtight container, layering the ice cream with the peanut butter cups.
Cover and freeze to set at least 4 more hours.
Best eaten within 2 days.