In a saucepan over medium low heat, warm the milk and 1 cup of the heavy cream. While this is warming, set up an ice bath (a large bowl of ice with a smaller empty bowl set within it) and pour the remaining cup of heavy cream into the empty bowl.
In a medium sized bowl, combine the sugars, egg yolks, and egg. Whisk thoroughly until the mixture turns a pale yellow color. Add the cocoa powder and pinch of salt then whisk thoroughly.
Once the milk and cream mixture has begun to steam, slowly stream about half of the liquid into the sugar/egg mixture while whisking constantly to temper the eggs.
Pour the tempered liquid back into the saucepan. Turn the heat to medium and while stirring constantly, cook the ice cream base until it thickens enough to coat the back of a spoon or looks almost like a pudding. Remove from the heat, place a strainer over the bowl with the cream, and pour the cooked base into it.
Cover directly on the surface with plastic wrap to cool. If possible, place the entire ice bath in the refrigerator.
Once the ice cream base has chilled, add the vanilla extract then churn it in an ice cream machine following the manufacturer’s instructions. Chop the brownies into small bite size pieces and place in the freezer.
With about 5 minutes left until the ice cream is ready, add the brownie chunks. Other methods include churning the ice cream completely then stirring in the brownie chunks in by hand or alternate layers of ice cream with brownie bits in the freezer safe container.
Scoop the ice cream into a freezer safe container, cover with plastic or wax paper and freeze until hardened. Set out on the counter about 5-10 minutes before serving for ease of scooping.