Wash and pick any stems from the blackcurrants. Transfer them to a blender with the milk. Blend until no solids remain, and then strain through a fine-mesh strainer to remove the seeds.

In a medium pan, combine the currant puree, cream, salt, honey, sugar, and Crème de cassis. Heat over medium-high, whisking often, until just before it starts to boil or about 175 degrees. Turn off the heat. 

In a small bowl, whisk the egg yolks until blended. Add a ladle full of the hot milk and cream mixture to the yolks. Whisk continuously for about 20 seconds to prevent the yolks from having a chance to cook. Pour this back into the pan, put the heat back on, and continue cooking until the mixture has thickened and reached about 180 degrees.

Transfer the ice cream mixture to the fridge to cool completely. This will take a few hours, but you could do it the day or night before you're ready to make the ice cream. Meanwhile, put your ice cream maker base in the freezer (if not already there) and a metal loaf tin or other storage container. 

When the ice cream custard base has cooled, get your ice cream maker ready to go. Turn it on and pour in the base mixture. Let churn for about 20-25 minutes or until the directions for your maker suggest for a typical recipe. When the ice cream has thickened up, and it's nearly done, add in the chocolate chunks.

If you like soft-serve ice cream, you could enjoy the ice cream immediately. Otherwise, scoop it into that frozen tin, cover it with plastic wrap, and freeze for at least two hours for a hard ice cream consistency. The longer you freeze it, the harder the ice cream will be.