In a 3 quart sauce pan, melt chocolate over low heat, stirring constantly. Slowly whisk in milk into melted chocolate. Stirring constantly, heat until thoroughly combined into a smooth mixture. Remove from heat and set aside.
In a large mixing bowl, use a hand mixer to whisk eggs until light and fluffy, 2 to 3 minutes. With mixer running, slowly add in sugar until completely incorporated, about 1 minute. Add cream, vanilla and salt and mix to combine. Pour in cooled milk and stir to combine. Cover and refrigerate until cold, 2 to 3 hours.
Transfer mixture to a 1-1/2 quart ice cream maker, and, following manufacturers instructions, allow maker to freeze mixture into ice cream. Makes 1-1/2 quarts.