In a clean quart jar, combine the coffee, chicory, and 675 grams of the water. Seal the jar, shake it, and leave it out of direct sunlight overnight.
Meanwhile, make the sweetener: In a wide-mouth plastic squeeze bottle or glass pint jar, combine the honey, agave, molasses, and remaining 100 grams water. Shake until everything is thoroughly combined. The syrup will keep for at least a couple of months in the refrigerator.
When the coffee is ready, give the jar a couple of shakes, then strain through a fine-mesh sieve into a large liquid measuring cup. Clean the jar and the sieve, then line the sieve with several layers of cheesecloth. Pour the coffee back through the lined strainer to remove any remaining sediment. Lid up the jar and store in the refrigerator for up to 1 week.
To serve, combine 4 fluid ounces (1/2 cup or 120 grams) of the coffee with 1 tablespoon (15 grams) of the sweetener (add more if you like it sweeter) in a pint glass, then fill the glass with ice. Top off with milk and stir.