In a medium bowl, mix the remaining 2/3 cup sugar and 1 cup whole milk until the sugar is dissolved. Then add the vanilla, heavy cream, and the juice from the strawberries. (You can also add food coloring if desired). Mix well and pour into your ice cream maker. When soft-serve consistency is reached, add the sliced strawberries and let the ice cream maker run for a few more minutes, until strawberries are incorporated throughout the ice cream. Remove from the ice cream maker and place in an airtight container in layers, drizzling the melted chocolate over each layer. Put in the freezer for several hours to allow ice cream to firm up.