Place ground coffee in filter basket of a drip coffeemaker. Add 2 cups cold water to water reservoir and brew according to manufacturer's directions.
In a small saucepan, combine coffee and sugar; bring to a boil. Reduce heat; simmer until reduced by half, about 30 minutes. Remove from heat; transfer to a small bowl or covered container. Refrigerate, covered, until cold or up to 2 weeks.
To prepare coffee milk: In a tall glass, mix 1 cup milk and 2-4 tablespoons coffee milk syrup.
