Place chocolate bar and fudge topping in top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula, until melted, about 5 minutes. Mix in 1/2 cup milk and hot chocolate mix. Remove from heat and cool to room temperature, 10 to 15 minutes.

Pour cooled mixture into a blender. Add remaining 1 cup milk and ice cubes. Blend to milkshake consistency, 1 to 2 minutes.