Combine the milk and cream together in a medium bowl. Heat it in the microwave for 1 to 1.5 minutes, until very hot. Or pour it into a pot and use the stovetop.
Add the chocolate chips, sugar, and use a sifter or sieve to add the cocoa powder. Gently mix the ingredients and then just let it sit for 5 to 10 minutes. This will allow the sugar to dissolve and the chocolate chips to melt.
Add the vanilla extract and whisk the mixture well until all combined and the mixture is smooth. Cool the mixture down to room temp or place in the fridge to cool down. If it is warm it will take much longer to harden up, in the homemade ice cream maker.
Make the homemade ice cream maker by pouring the ice cream base into a ziplock freezer bag. Then place ice in another freezer bag. Place the ice cream bag inside that bag and then pile on more ice. Add a half of a cup of rock salt and close it up. Then, wrap it with a towel, since it will be really cold, and shake for 5 to 10 minutes until it hardens. It won't get completely hard, but more of a soft-serve consistency.
Place the ice cream into a freezer-safe container and add a bit of plastic wrap to the top. Press it down right on the top. This will keep ice crystals from forming. Freeze for 4 to 6 hours or overnight before serving. Enjoy!