Pour ground coffee into a French press and add water. Place plunger lid on top and press the plunger down 1 to 2 inches to make sure all coffee grounds are fully submerged; do not press all the way down. Let coffee steep at room temperature for 16 to 18 hours.
Strain coffee through a coffee filter in a small strainer. Transfer to an airtight bottle or jar and keep in the fridge for up to a week.
To serve, fill a glass with ice, and add equal parts of cold brew and water or milk.