Slice the onions in a food processor or by hand and place them in a mason jar. You may need more than one jar depending on how many onions you use.
Warm up ½ cup of water and add the salt to it. Stir until the salt dissolves. Add the rest of the cold water to the salt mixture. Once the brine has cooled to room temperature, add it to the jar with the onions. Make sure to cover the onions completely in the brine. Cover and let sit on the counter for 5-7 days before placing in the refrigerator.
Notes
You can taste the onions as they ferment on the counter and place them in the fridge once they have developed a flavor that you like. I usually taste them after 4 or 5 days and then leave them out longer if I want them to develop a more sour, pickly flavor. These will last in your fridge for up to a year.
Recipe by Fermented Food Lab at https://www.fermentedfoodlab.com/pickled-onions/