Heat milk in a saucepan until it just begins to bubble. Be careful not to let it boil.
Meanwhile, whisk the eggs together with the sugar until they light and fluffy.
Beat cocoa into the egg mixture.
Pour about 1/2 cup of hot milk over top of the egg mixture. Mix together well.
Pour this egg/milk mixture back into the saucepan and continue to heat, stirring constantly until the mixture begins to stick to the back of your spoon and becomes very thick.
Stir in finely chopped bittersweet chocolate and stir until the chocolate melts completely.
Remove from heat and cool mixture.
After mixture has cooled, transfer it to the fridge and chill for at least 2 hours.
Blend in the whipping cream and vanilla.
Pour chocolate mixture into your ice cream machine.
Mix in ice cream maker for 25-30 minutes or according to manufacturer's instructions.