Heat cream, milk, sugar, espresso, and salt in a medium-sized saucepan over medium heat.
Stir constantly, until the mixture just reaches the point of simmer. Then remove from heat.
While cream/milk mixture is heating, lightly whisk the egg yolks in a separate medium-sized heat-proof bowl.
Slowly pour about half of the warm milk/cream into the bowl with the egg yolks, whisking while you do so.
Then pour the egg/milk mixture back into the pan with the rest of the milk.
Continue to cook over low heat, while whisking. When the mixture thickens enough to coat the back of the spoon, after about 5-7 minutes, remove the saucepan from heat.
Strain the egg/milk mixture into a separate large bowl.
Cover bowl with plastic wrap, making sure plastic wrap is touching top of liquid so skin does not form, and refrigerate for at least 4 hours.
Once mixture is chilled, freeze in an ice cream maker according to the manufacturer’s instructions, mixing in brownie pieces when ice cream is almost done processing.
Remove ice cream to airtight containers and put in freezer for at least 4 hours to continue to harden.