Scrub the burdock root with a vegetable brush, scratching a little of the surface peeling off. Prepare a bowl of 4 cups of water and add the vinegar. Cut the ends off and throw away (compost). Cut a section about 1 1/2 inch long, then slice in half the long way, cut into matchsticks. After cutting put in the water with vinegar. After cutting half the burdock, I change the water, adding vinegar again. Let soak about 10 minutes after cutting.
Scrub the carrot and cut into matchsticks also. It doesn't have to go into the water with vinegar..
Microwave or blanche the carrots in a spoon of water. Drain. But I like raw carrots.
Cover the burdock in water and boil for about a minute, taste, if you feel the taste is too strong, boil a little longer, another minute. You don't want to boil the 'earthiness' away. Drain.
Mix the Mayonnaise Dressing. I like to keep the sodium down so if you need more, you could add the soy sauce, but if your mayonnaise is too runny, then just use more salt.
Put burdock, carrots, corn and cabbage (if using) in a large bowl. Add most of the dressing. Vegetables should be lightly dressed, add rest of dressing as needed. Cool in the refrigerator for an hour or two.
Note* BURBOCK will probably be sold in the root section of the store or your farmer's market. It is usually fresher if you can find it covered with dirt like a potato. Or in the prepared veggie section, it might be washed, possibly cut in half (to shorten to fit into a sack) but with the peeling still attached. Or in some Asian markets you may find matchstick-cut goboh which is all ready to cook (it will be in a transparent sack with liquid in it).
Note BURDOCK 2* I always used to peel the gobo but my chef friend showed me it wasn't necessary. If you are new to goboh or squirmish about the peeling, you can use a potato peeler, If you want really white goboh, trim the peeling down to the inner black circle (like a tree-ring). Also change the water once it turns dark, don't forget more vinegar.
Note 3* MAYONNAISE--If making your favorite recipe, make it a little thinner than usual. If using a bottled mayonnaise, I like to add lemon juice or water to thin. American-style mayonnaise is very thick. Japanese Kewpie Mayonnaise (no thinning necessary) comes in different proportions of oil in the mayonnaise--50 is 50% oil is cut; 75% is cut even more. It is very delicious, try it and you may not go back...Great on BLT and Koreans like to eat on French fries!