1.Stir together ground coffee and cold water in a pitcher until well combined.
2.Let stand at room temperature for 12 hours.
3.Pour coffee mixture through a large, fine wire mesh strainer into a Dutch oven or other large container, discarding grounds.
4.Clean strainer; place a coffee filter or double layer of cheesecloth in strainer. Pour coffee mixture through lined strainer into a pitcher.
5.Add vanilla extract. Cover and store in refrigerator up to 1 week, if desired.
6.Stir together coffee mixture and sweetened condensed milk.
7.Serve over ice.