If using an ice cream maker, freeze bowl according to directions (usually overnight or at least 24 hours in advance of use).Chop chocolate shards for mix-ins and freeze until ready to use.
Scald milk and heavy cream. In a medium sauce pot over medium heat, steep half of the orange zest and crushed cardamom pods in the heavy cream and milk. Bring it to a low boil, then reduce heat to low and simmer for 10 minutes, stirring occasionally.
Ribbon eggs and sugar. Whisk egg, egg yolk, and sugar together in a mixing bowl until light and fluffy, about 1-2 mins.
Remove the cardamom pods from the heavy cream with a fork or small strainer.
Temper. Slowly drizzle the heavy cream into the egg mixture while whisking constantly to prevent the eggs from scrambling. Once about half the heavy cream has been added, you can pour faster, but don't stop whisking!
Cook to thicken. Transfer the mixture back to the pot over low heat. Stir with a wooden spoon, scraping the bottom well, until it thickens and coats the spoon. If you tilt the pot you should see a smooth layer coating the bottom of the pan.
Strain any lumps. Remove from heat and strain into a heat-proof, airtight container.
Chill. Cover and let cool at room temperature 1 hour, then in the fridge for at least 3 hours or overnight before churning.
Churn. Pour ice cream mixture into base of your chilled ice cream maker and let it run until ice cream has formed (this can take up to 20-30 minutes, depending on your ice cream maker). If your ice cream maker has a hard churn setting, add frozen chocolate chips in the final stage of churning. Otherwise, proceed to next step. Add mix-ins. When ice cream maker is done, transfer the ice cream mixture to an airtight container. It will still be fairly soft at this point. Chill for an hour in the freezer, then use a spatula to mix the frozen chocolate shards until they’re evenly distributed. Cover and chill at least 2 hours before scooping.