In large dish with pour spout whisk together water and sea salt, stir to dissolve. Set aside.
Place Brussels sprouts, garlic and ginger into preferred fermenting container(s). (See fermenting container options below in Recipe Notes.) Pack pieces in tightly (to the neck if using canning jars).
Pour salted water over Brussels sprouts. Press firmly on solids, so water rises above and air bubbles are released. You want the brine to come about 1/2-1 inch above the vegetable pieces but still leave 1 inch head space if using jars.
Weight with fermenting weights (see link below in Recipe notes) or preferred weight.
Lightly seal lid(s), and place in warmest location possible for 7-14 days, depending on warmth of location. Check the veggies every 2 days or so to make sure they're staying below the brine.
They're done when the liquid is no longer very bubbly, when the Brussels sprouts are nicely tart/vinegary, to your taste.
Transfer to refrigerator, and serve as a condiment. The flavor will continue to improve and develop. Any extra brine you don't wish to drink can be used to ferment in other recipes. (See my Sourdough Grain-free Waffle recipe. The brine is used to reduce phytates in cassava flour. It's great to have extra brine on hand!)