Pour the coarsely ground coffee in a large carafe or jar. Add the filtered water. The grounds will rise to the surface of the water.
Gently stir together the coffee and water so that all the coffee grounds are well saturated. Cover with a tight-fitting lid.
Place in the refrigerator for 18-24 hours.
Line a sieve with cheesecloth, a flour sack towel, or a large coffee filter. Place it over a large glass measure, 4 cup capacity or greater. Slowly pour the coffee through the sieve.
When all of the coffee is filtered through, discard the coffee grounds. Pour the coffee concentrate into a large container with a tight-fitting lid. Cold brew concentrate will keep for up to 2 weeks in the refrigerator.
To serve, fill an 8 oz. glass with ice cubes. Pour in 1/2 cup of coffee concentrate. Add up to 1/2 cup of cold water to dilute. Add flavored syrups, sweeteners, and creamers to taste, if desired.