Zz, sorry I don't have an exact recipe for you.
We were given this gigantic head of garden fresh bok choi about the size of four gallons of milk, and my mother and I had a brief brainstorm of how to deal with it. She nixed my question about freezing whole leaves. Although creamed soups do typically use a lot of veggie to make, I was skeptical about her idea of pureeing a water-heavy white-fleshed cabbage. Couple days later, with a bug in my nose, I slept through a morning to wake up to my mom's bubbling pan. It tasted good, so I asked how she made it.
Sweat and wilt some chopped green onion, shaved celery and a pot full of bok choi, ours having large and very dark green leaves, in a little peanut oil. A better than average batch of chicken stock. Reduce heat, add some leftover rice (not too much) and cook while stirring until liquid starts to thicken like a risotto. It's much like a porridge in Japan called okayu, often served to someone under the weather. Puree in a blender, return to heat, season to taste. She admitted that the taste was a bit thin and that the soup got some extra salt and shot of sesame oil. No dairy.
PF, taki is "to burn, cook" and komi is "to include, join." It's very common to cook rice with ingredients other than water. The simplest is blanched peas, dashi stock, a little sake and salt. Every Japanese household cooks matsutake gohan in one form or another. I'm not sure of the etymology of "kayaku." It's not a brand, but the combination of ingredients is so common that the rice preparation has gotten its own name. The added ingredients are pre-cooked in 2:1 soy:sake, the cooking liquid is diluted with water or dashi 1:2. Some people will sweeten it, others might sour it up a bit.
If you can't find burdock root, I might try the following substitution, though I haven't tried it -- the tough ends of asparagus. It's somewhat close in texture and taste. Skin it, and whittle it, like with a boy scout knife, into small slivers.