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Add the water to a large pot and bring it to a boil. Then pour the hot water into a large bowl and add the salt and one Tbsp. of the brown sugar. Allow the water to cool.
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Once the water has cooled, add in the cabbage, daikon, and carrots, and place them in the brine. Place a cover on top of the bowl (using a heavy book, or heavy stable item on top to keep the cover weighted down and the vegetables submerged in the brine. Brine the vegetables for about 12 hours.
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To make the paste, mix the chili flakes, Lee Kum Kee Panda Brand Premium Cooking Soy Sauce, Lee Kum Kee Pure Sesame Oil, remaining brown sugar, ginger, and Lee Kum Kee Minced Garlic.
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Drain the vegetables from the brine. Using plastic gloves, massage the paste into the vegetables. Mix in the sesame seeds. When everything is combined, transfer the kimchi to sterilized jars. Be sure to pack the kimchi down so there are no air bubbles and the vegetables are submerged in the juice. If not, add a little extra brine to the jar. Top with a lid and Garlic Sesame Kimchi is ready to eat!