I found burdock root in my local Asian (mostly Chinese) supermaket for the first time last week. It doesn't really look especially edible to my English mind, but it is absolutely delicious.
I used it in a recipe called kinpira gobo, in which the burdock root is cut into thin matchsticks, with similarly cut carrot, and fried for a few minutes. I then added a mixture of sake, sugar and soy sauce and cooked it for a few minutes longer. I then took it off the heat and added some crushed roasted white sesame seeds. I think it's usually eaten hot, but I like it cold or at room temperature, too. I might have got the recipe a bit wrong, but it tastes rather good. I must get some more burdock tomorrow and make it again...
Incidentally, I had only ever heard of burdock before in a drink called dandelion and burdock - perhaps the English equivalent of the American root beer. I suspect that the drink has generally never even been near any dandelion or burdock these days. But it's still tasty.