Whisk together cocoa and sugar in a heavy saucepan. Slowly whisk in milk and 1 cup of the cream, then whisk in egg yolks. Whisk till smooth.
Cook and stir over medium heat till temperature reaches 170-175°. Mixture should barely come to a boil.
Remove from heat and add salt, chocolate chips, and vanilla. Stir till chocolate is totally melted and mixture is smooth.
Pour through a fine meshed strainer to remove lumps, then stir in remaining cup of cream. Chill for several hours or overnight. Prepare cookie dough, break into small chunks, and freeze.
Freeze ice cream in an ice cream maker according to manufacturer's instructions. Pour into a freezer safe container and stir in cookie dough bits.
Freeze ice cream for 4 hours or till stiff enough to scoop.
For cookie dough:
Beat together butter, brown sugar, dry pudding mix, and vanilla in a small bowl.