Scald 200 ml. of milk in a pan.
Stir the egg yolks and 1/2 c. of sugar in a bowl. Pour the scalded milk in a thin stream, mixing as you pour. Your tempering the egg yolks so go slow with the pouring to prevent the egg yolks from cooking.
Pour the egg yolk mixture back into the pan. Set the heat to medium-low and cook, stirring, just the until the mixture thickens and coats the back of a spoon. Turn off the heat at once and stir in the remaining 200 ml. of milk and cream to prevent the eggs from cooking any farther. Pour into a covered container and chill for a few hours in the coldest part of your fridge (normally, at the back of the bottom rack).
Place the remaining half cup of sugar in a clean pan. Add 1/4 c. of water. Boil until the sugar melts without stirring. Lower the heat to medium and continue to boil until syrupy. Do not wait for the mixture to darken — you just want it to thicken.
While the syrup boils, chop the bananas. In a bowl, toss with lemon juice to prevent discoloration. Pour the syrup over the bananas and stir. Puree in the blender, pour into a covered container and cool. Chill in the fridge.
When the egg mixture and bananas mixture are both well chilled, you’re ready to process them in your ice cream maker. To synchronize everything, prepare the chocolate mixture before you start making your ice cream.
Break the chocolate into small pieces and melt over simmering water in a double boiler (or, about one minute in the microwave oven). Stir in the 4 tbsps. of milk little by little making sure that the mixture stays smooth and silky.
Now, make the ice cream. Pour the egg mixture into the ice cream maker compartment. Halfway through the processing time, pour in the banana mixture.
When the ice cream is done and while it is in soft-serve stage, transfer to a wide shallow bowl. Pour the chocolate mixture in a thin stream, cutting and folding the ice cream as you pour.
Enjoy the chocolate and banana ice cream soft-serve style or freeze for a couple of hours for a firmer ice cream.