Toast the marshmallows under a broiler or with a chef torch.

In a saucepan combine the milk, cream, and 1/2 cup sugar over medium heat. Cook until the sugar dissolves, about 5 minutes.

Meanwhile, in a medium bowl whip the egg yolks with the remaining sugar using an electric mixer until the eggs have become thick and pale yellow, about 4 minutes. Pour 1/2 cup of the warm milk and cream mixture into the egg mixture and stir. Add this mixture back into the saucepan. Cook over very low heat, stirring constantly, until the mixture becomes thick enough to coat the back of a wooden spoon, about 7 to 10 minutes.

Place a strainer over a medium bowl and pour the warm custard mixture through the strainer. Stir in the marshmallows until they dissolve. Chill mixture completely before pouring into an ice cream maker and follow manufacturer's instructions to freeze.

In a medium saucepan, bring the water, cocoa powder, and corn syrup to a boil. Reduce the heat then simmer for 3 minutes, stirring frequently. Remove from the heat and add the chopped chocolate. Stir until completely melted. Cool to room temperature then store in the fridge until ready to assemble the ice cream.

To assemble, place half of the ice cream into the bottom of a container. Pour the fudge sauce on top then add the remaining ice cream. Freeze at least 1 hour before serving.