Whisk the eggs with the sugar until light and fluffy (an electric mixer quickens the process). Add milk and cream. Incorporate and add cocoa and vanilla extract. Mix to dissolve all cocoa. If you wish to add melted chocolate, add it now. This will change the consistency of the ice cream. The melted chocolate will harden into tiny bits, giving a grainier result.
2 ½ cups whole milk, 2 ½ cups heavy cream, 1 cup granulated sugar, ¾ cup Dutch-process cocoa powder, 2 large eggs, 1 teaspoon vanilla extract, 4 ounces melted semi-sweet chocolate (optional)
Chill the mixture for 2-4 hours. This will ensure a better freeze. Follow the manufacturer’s instructions for your ice cream freezer. My KitchenAid attachment takes 20-30 minutes. Once frozen, promptly place it in a freezer container and put it in the freezer for 2-4 hours for hard-style ice cream. Or enjoy as soft serve right away.