In a separate vessel, make a brine by combining the water and salt.
Place a weight, if using, then pour the brine into the jar, leaving at least 1 inch of headspace. Screw the lid on tightly and store the jar in a warm spot away from direct sunlight to ferment for 2 weeks. Burp the jar daily to relieve pressure by removing the lid for a few seconds, then screwing it back on.
Once fermentation is complete, strain the ferment, reserving the ¼ cup of brine.
In a blender or food processor, combine the ferment, vinegar, reserved brine, turmeric, and mustard. Blend until smooth.
Keep the sauce stored in the refrigerator for up to 1 year.