Grind the whole coffee beans on the coarsest setting of your burr grinder until they look like coarse sea salt.
Add the grounds to the bottom of the French press, then pour the cold filtered water over them in a slow circle.
Stir gently for 10 seconds with a wooden spoon to ensure all grounds are fully wet, then place the lid on with the plunger completely up.
Steep on the counter at room temperature for 12 to 14 hours (or in the refrigerator for 20 to 24 hours).
Press the plunger down slowly with steady, even pressure until it reaches the bottom.
Pour the cold brew concentrate immediately out of the French press into a clean glass jar for storage, leaving the spent grounds behind.
To serve, dilute 1/2 cup of concentrate with 1/2 cup of water or milk over ice.