Heat the milk and cream. In a small saucepan over medium heat, warm the milk, cream, ½ cup of the sugar, cocoa, vanilla, and salt until steaming, about 170°F.
Beat the eggs and remaining sugar. In a separate bowl, beat the egg yolks and remaining ¼ cup of sugar until they are light yellow and form a ribbon when the beaters are lifted, about 2-3 minutes, with a hand mixer on low speed.
Temper the eggs. Slowly whisk half of the warm milk mixture into the beaten egg yolks, adding half a cup at a time to prevent curdling. Then, pour the egg mixture back into the saucepan with the remaining milk and cream.
Heat the custard. Heat the saucepan over medium heat, stirring constantly, until the custard thickens and reaches 185°F. The custard is ready when it coats the back of a spoon.
Strain the custard and chill. Strain the custard through a cheesecloth or a fine-mesh strainer into a bowl. Place the bowl in the refrigerator and chill for 4-24 hours until the custard is very cold.
Freeze ice cream. Freeze the chilled custard in your ice cream maker according to the manufacturer's instructions. Once it reaches a soft-serve consistency, transfer the ice cream to a loaf pan, cover it with plastic wrap, and freeze until firm. The ice cream will stay in the freezer for up to a week.