Separate the cabbage leaves from the base, wash and pat dry. Pile a few leaves into a stack. Slice the stacks length-wise, then rotate and chop into 2-inch pieces.
Peel the carrot. Shave the remaining carrot into long slivers, then cut the slivers in half. Seed and dice the chili peppers.
In a medium saucepan, bring the rice wine vinegar, sugar, sliced ginger, and salt to a boil over medium to medium-high heat. Once it comes to a boil, turn off heat and set aside.
Combine the cabbage, carrots, and peppers in a large bowl or container, preferably with an airtight lid (I use a large Tupperware so that I can just put on the top and shake.). Pour the hot vinegar mixture on top, then toss until every piece is thoroughly coated. Refrigerate for at least 4 hours, tossing occasionally, or overnight.
Note: The cabbage will wilt and release a lot of liquid in the process of chilling, so I use a slotted spoon when serving.