Stir together ground coffee and 8 cups cold water in a pitcher until well combined; let stand at room temperature 12 hours.
Pour coffee mixture through a large, fine wire-mesh strainer into a Dutch oven or other large container, discarding grounds. Clean strainer; place a coffee filter or double layer of cheesecloth in strainer, and pour coffee mixture through lined strainer into a pitcher. Add vanilla extract. (Cover and store in refrigerator up to 1 week, if desired.)
Stir together coffee mixture and sweetened condensed milk. Serve over ice.