In a medium-sized saucepan, heat heavy cream, milk, granulated sugar, and vanilla over medium heat, stirring constantly for about 5 minutes, or until the mixture begins to bubble. Remove from heat and transfer the mixture into a large bowl. Allow to cool for about 1 hour.

Once the mixture is cooled, cover with plastic wrap and place in the refrigerator for at least 8 hours or overnight.

After chilling, give the ice cream a quick stir. Churn the mixture in an ice cream maker, according to its instructions.

While the ice cream is churning, the chocolate "chips" can be made. Combine the chocolate chips, butter, and water in a microwave-safe bowl and microwave in 20-second intervals, stirring in between each interval until the mixture is melted. Pour the chocolate mixture into a ziplock bag and cut a small hole in the corner. 5 minutes before the ice cream is done churning, begin drizzling the chocolate mixture into the ice cream.

After the ice cream is churned, it will be very soft and should be poured into a closed container and frozen for at least a few hours before enjoying. This ice cream lasts about 3-4 days.