Dissolve 1 tsp (5 mL) salt in 1 cup (240 mL) water and set aside.
Remove any bruised outer leaves of cabbage. Cut cabbage into quarters then remove and discard the core sections. Slice quarters into 2 ½ in. (6 cm) -wide ribbons and place in a large bowl, then sprinkle with 1 Tbsp (15 mL) salt. Massage salt into cabbage, squeezing to release liquid. Cover bowl and let stand 1-2 hr.
Process garlic, chili flakes, ginger, fish sauce, and soy sauce in a food processor until a paste forms. Add carrots and green onions to cabbage. Add chili paste mixture and massage to combine.
Pack kimchi into the jar, tamping down firmly with a spoon. Leave at least 2 in. (5 cm) of headspace. Pour any liquid collected in the bowl over the kimchi, pressing down firmly to help liquid cover the cabbage. There may not be a lot of natural brine at this time, but the cabbage will continue to release it slowly.
Place spring on top of cabbage, then twist lid on.
Wipe jar down and cover with a cloth. Store in a cool (68°F-72°F or 20°C-22°C) place for 24-36 hours. If after this time the brine does not cover the cabbage by 1 in. (2.5 cm), remove lid and spring, add some additional brine to cover. Wipe jar rim before replacing spring and lid. Discard remaining reserved brine.
Check daily to make sure vegetables remain submerged in brine.
Let kimchi ferment for 1 week, then taste for the mild tangy flavor. If flavor is to your liking, proceed to step 9. If you prefer a stronger flavor ferment up to 1 additional week, tasting every 3 days, until flavor develops.
Once desired flavor is reached remove spring and add fresh brine as necessary to cover. Wipe jar rim before replacing lid or use a Ball® canning lid. Store in refrigerator up to 6 months.