Heat-treat the flour by spreading it on a baking sheet and baking at 350°F for about 5 minutes. Let it cool completely.
Make the cookie dough by beating the softened butter, brown sugar, and granulated sugar until smooth. Mix in the vanilla and milk.
Add the cooled flour and salt. Stir until a soft dough forms, then fold in the mini chocolate chips
Portion the cookie dough into small pieces and place them on a parchment-lined plate or baking sheet. Refrigerate or freeze while preparing the ice cream.
Add the heavy cream, whole milk, sugar, espresso powder, and salt to a saucepan. Warm over medium-low heat, whisking until the sugar and espresso dissolve. Do not boil.
Remove from the heat and stir in the vanilla extract. Transfer the mixture to a bowl and refrigerate until thoroughly chilled, preferably for at least 2 hours
Pour the chilled espresso mixture into an ice cream maker and churn according to the manufacturer's instructions until thick and creamy.
Layer the churned ice cream with the chilled cookie dough pieces and espresso chocolate chips in a freezer-safe container.
Gently fold the additions into the ice cream, being careful not to overmix.
Cover tightly and freeze for 4 to 6 hours, or until firm enough to scoop.
Let the ice cream sit at room temperature for 5 to 10 minutes before serving.
