Pour 2 cups of milk into a medium saucepan.

Bring the milk to a simmer over medium heat.

Remove the saucepan from the heat.

In a separate bowl, combine the remaining 1 cup of milk, sugar, cornstarch, and cocoa powder.

Mix the ingredients together until well combined.

Add the milk mixture to the hot milk in the saucepan.

Cook over medium heat, stirring continuously until the sugar and cocoa dissolve and the mixture thickens slightly.

Remove the saucepan from the heat and let the mixture cool to room temperature.

Once cooled, cover the mixture and refrigerate overnight or for at least 8 hours.

Pour the chilled mixture into an ice cream maker.

Process the mixture according to the manufacturer's instructions.

During the last 2-3 minutes of churning, add the optional crushed chocolate cookies or mini chocolate chips, if desired.

Once churned to a gelato consistency, transfer to an airtight container and freeze for at least 2 hours to harden further before serving.