1) Whisk or mix together the milk, sugar, espresso powder, and cocoa till the sugar has dissolved.
2) Stir in the heavy cream and vanilla.
3) Freeze in ice cream maker according to manufacturer's directions.
4) Stir cookie bits into soft ice cream, and serve immediately.
5) For firmer ice cream, place in a covered container. Place in the freezer for 2 to 3 hours, until ice cream is as hard as you like it. Note: Freezing longer than this will make the ice cream rock hard; plan on softening at room temperature for 15-20 minutes or so before serving, if the ice cream has been in the freezer longer than a few hours.
6) Don't have an ice cream maker? Simply pour the chilled mocha cream into a bowl, place the bowl in the freezer, uncovered, and stir the cream every hour. After about 4 hours or so, it'll be soft-serve consistency. Continue to stir and freeze till it's the consistency you like. While it won't be as creamy as churned ice cream, it'll be absolutely delicious. After 6 or more hours in the freezer, it'll become quite hard. To serve, simply remove from the freezer for 15 minutes or so, to soften it enough to make it "scoopable."