Combine the ground coffee and water in a large jar or pitcher. Pour the water in a slow, steady stream while stirring gently to make sure all grounds are wetted.
Add the vanilla extract, if using, and give the mixture one more gentle stir. Cover the container with a lid or plastic wrap.
Let the coffee steep undisturbed in the refrigerator for about 16 hours (12–20 hours will work depending on how strong you like it).
Line a fine-mesh sieve with a double layer of cheesecloth or a paper coffee filter and set it over a clean jar or bowl. Pour the steeped coffee through the sieve slowly to separate most of the grounds.
For a clearer concentrate, strain the coffee a second time through a fresh paper filter or a very fine mesh. Gently press with a spoon—don't force—so you don't push fine sediment through.
Transfer the finished cold brew concentrate to an airtight container and refrigerate. Serve over ice diluted to taste (common ratio 1:1 concentrate to water or milk), then sweeten if desired.
Store leftover cold brew refrigerated for up to 10 days; shake gently before using as the concentrate can settle.