In a heavy-based saucepan, combine the milk and cream. Sift the cocoa powder over the mixture; whisk thoroughly to combine. Sprinkle about half the sugar into the saucepan and slowly bring the mixture to a simmer; don't let it boil.
Put the chopped chocolate in a medium bowl and fill a large bowl with ice water.
While waiting for the milk mixture to simmer, whisk the egg yolks with the remaining sugar. Whisk vigorously until the yolks thicken and become a paler shade of yellow, 3 to 4 minutes.
To combine the egg and milk mixtures, slowly pour half the simmering milk into the yolks while whisking constantly to temper it. Whisk that mixture back into the milk in the saucepan. Reduce the heat to low and stir constantly with a wooden spoon or rubber spatula in a figure-eight motion until the custard is thick enough to coat the back of a spoon (about 170°F), 10 to 15 minutes.
Pour the cooked custard over the chocolate. Whisk until all the chocolate is melted. Set the custard bowl over the bowl of ice water; stir until the custard is completely cool. Pour through a fine sieve if there are any lumps and then refrigerate for several hours or overnight.
Pour the custard into an ice cream machine with at least a 1-quart capacity and freeze following the manufacturer's directions.