In a medium pan, combine the milk, cream, ¾ cup of the sugar, unsweetened chocolate, cocoa powder, and salt. Cook over medium-low heat, stirring frequently, until the chocolate is melted and small bubbles start to appear around the edges of the pan.
Meanwhile, in a large bowl, beat the eggs until they turn light in color. Gradually add the remaining ¼ cup of sugar to the eggs while beating on low speed or whisking by hand.
When the chocolate mixture is hot, gradually whisk about 1 cup of the hot liquid into the eggs to temper them.
Pour the tempered egg mixture back into the saucepan with the hot liquid and continue to cook and stir over medium-low heat until the mixture reaches 175° F or is thick enough to coat the back of a spoon. Remove from the heat and stir in the vanilla.
Remove from heat and allow to cool completely, then transfer to a bowl or heavy duty zip tight bag and place in an ice water bath until completely cold. Alternatively, chill the ice cream base in the fridge overnight.
Once thoroughly chilled, pour the chocolate base in an ice cream maker. Insert the paddle attachment and churn until frozen and about the consistency of soft-serve ice cream. Fold in brownie pieces or other solid mix-ins right at the end, if using.
Transfer half of the ice cream to a container, then top with half of the fudge sauce. Repeat with the remaining ice cream and fudge sauce. Freeze for at least 4 hours to cure for hard ice cream.