Add 1 cup heavy cream and vanilla to a large bowl with a mesh strainer set on top.

Combine whole milk, 1/2 cup heavy cream, sugar, cocoa powder and salt in a medium saucepan, cooking over medium heat until sugar has dissolved. Cook, stirring occasionally, until heated through and steaming.

In a small bowl, whisk eggs. Slowly drizzle 1 cup hot liquid into egg yolks, whisking continuously. Return egg mixture to saucepan. Cook until mixture coats the back of a spatula or wooden spoon. Add chocolate, stirring until melted and mixture is smooth. Pour through a mesh strainer into remaining heavy cream. Place bowl in an ice bath, stirring until cooled. Cover and chill thoroughly, 4-6 hours or overnight.

Using a 1 1/2Qt ice cream maker, churn according to manufacturer's directions. Add 1 cup chocolate cookie pieces in the last 5 minutes of churning. Transfer to a freezer safe container, cover and freeze until firm, at least 4-6 hours or more.