Step 1

In a saucepan, whisk together the cream, milk, brown sugar, granulated sugar, cocoa powder, egg yolks, espresso powder and salt. The mixture will look lumpy, but it will smooth out as you cook it.

Step 2

Over medium heat, warm the custard while whisking constantly, just until it begins to steam and is barely bubbling around the edges. Don't let it come to a boil.

Step 3

Remove from the heat and whisk in the vanilla and the chopped chocolate until smooth. Pour the custard through a mesh strainer to remove any bits of cooked egg. (To ensure a very smooth texture, you can use an immersion blender to blend the custard for 15 seconds.) Cover the bowl of custard, with plastic wrap resting right against the surface of the custard, and refrigerate until well chilled, preferably overnight.

Step 4

Pour the chilled custard into your ice cream maker and churn according to the manufacturer's instructions, until it has a soft-serve consistency. During the last minute of churning, add the bourbon.

Step 5

Scrape the ice cream into a lidded container and freeze until firm, at least 8-10 hours.