In a medium saucepan, whisk together heavy cream, whole milk, granulated sugar, instant espresso powder, and salt.
Heat the mixture over medium heat until it begins to steam.
In a separate mixing bowl, whisk together egg yolks and vanilla extract.
Slowly pour the heated mixture into the egg mixture, whisking continuously to combine.
Pour the mixture back into the saucepan and cook over low heat, stirring constantly with a rubber spatula, until the mixture thickens and coats the back of the spatula.
Strain the mixture into a large mixing bowl and let it cool for 10-15 minutes.
Cover and chill in the refrigerator for at least 2 hours or overnight.
Pour the mixture into an ice cream maker and freeze according to the manufacturer's instructions.
Once the ice cream is churned, fold in the crumbled brownies.
Transfer the ice cream to a baking dish and freeze for an additional 2-3 hours, until firm.