Combine 1/2 pound coffee grounds with 6 cups cold water in a large pitcher or glass jar. Let stand 5 minutes.
Add remaining coffee grounds and 3 cups cold water, making sure all the grounds are wet. Cover, and let steep, at room temperature for 12 hours or in the refrigerator for 24 hours.
Pass mixture through a fine sieve set over a medium bowl; discard coffee grounds. Line sieve with a standard coffee filter and pass mixture through again; discarding any remaining sediment. Pour coffee concentrate into an airtight container and refrigerate for up to 2 weeks.
To serve, dilute concentrate with an equal proportion of water or milk.