Dissolve 3 Tablespoons salt into 1 quart of water in a one-gallon glass or ceramic container. Stir until salt dissolves.
Quarter Brussels sprouts.
Shred and or slice carrots. (Or try both for a mixed texture).
Slice one of the leeks into 1" pieces.
Add all veggies to the brine. Add plastic lid or plate and weigh down (I use a glass wine bottle filled with water) so that the contents stay under the brine. Leave for 2 to 4 hours.
Drain the veggies through a colander, reserving a pint (500 ml) of the brine.
Add the mixture to a food processor and pulse until a slaw-like consistency (about 6-8 pulses). Work in multiple batches if needed.
Prepare spice paste
Roughly chop the garlic and slice the ginger. Add to bowl of a food processor bowl. If you don’t have a food processor, dice the ginger and garlic so it's almost a paste, and add to a mixing bowl.
Add pepper powder, soy sauce and a splash of fish sauce (to taste) to mixing bowl. Alternately to soy sauce, use reserved brine. Vegan variation: omit fish sauce.
Slice other leek into 1/2" pieces and add to mix.
Stir and mash contents (or pulse with food processor) together until a paste forms.
Pack Jar or Crock
Wearing a rubber, latex or plastic glove to protect yourself from the heat of the peppers, mix the paste thoroughly with your hand into the drained vegetables. You can mix everything directly in the fermenting container, or in a separate large mixing bowl. Mix until the veggies are coated nicely with the paste.
Ferment
Pack contents into a jar. Add a weight (glass fermentation weights, or a small jar filled with water) on top so that the contents stay under the brine. Some brine will continue to form once the veggies are pressed down.
Brussels sprouts tend to be drier than cabbage, so add some of the reserved brine to ensure the contents are submerged.
Cover with a cloth and secure with rubber band to keep flies out.
Store at room temperature for 4-5 days. Note: Your house will smell like kimchi.
Transfer contents to mason jars and continue to ferment in refrigerator for up to 6 months (if it lasts that long!)