Begin by chopping your 4 ounces of unsweetened chocolate. Place it in a double boiler or a microwave-safe bowl. If using a microwave, heat it in short bursts, stirring in between, until fully melted and smooth. Set aside to cool slightly.
In a mixing bowl, whisk together the 2 large eggs and 1 cup of sugar until the mixture is light and fluffy.
Slowly add the 1 cup of milk to the egg mixture while whisking continuously. After that, pour in the melted chocolate and mix until everything is well combined.
Transfer the mixture to a saucepan over medium heat. Stir continuously until the mixture thickens slightly and coats the back of a spoon, about 5-7 minutes.
Once thickened, remove the saucepan from the heat and stir in the 1 cup of heavy cream, 1 teaspoon of vanilla, and a pinch of salt. Allow the mixture to cool to room temperature.
Refrigerate the mixture for at least 2 hours or overnight.
Once chilled, pour the mixture into your ice cream maker and churn according to the manufacturer’s instructions, about 20-25 minutes.
Transfer the churned ice cream to an airtight container and freeze for at least 4 hours. Scoop and serve!