Dirty Soup was a big hit.

Sliced onion half rings sauteed in a mixture of rapeseed oil and sesame oil (the ubiquitous Kadoya brand)

Once they were nearly done I added a grated carrot and wafer thin slices of a large Jerusalem artichoke/sun choke and continued to saute for a little.

Freshly boiled water was then added as well as a chopped leek and some sliced cabbage leaves. Once this had simmered enough so that the cabbage was just right I added miso and turned off the heat.

Yesterday evening's leftover brown rice was put in a couple of bowls and the soup ladled on top.

As you said, absolutely no need whatsoever for dashi. It was delicious. Second helpings all round.
And the Jerusalem artichoke slivers seemed to be a perfect substitute for burdock root.

Of course, despite MrLapLap praising the result (he went and had a third bowl), he also confided that this was pretty much the omiso shiru kake gohan that formed the bulk of obaasan's dogs' diets.

Really easy to do though, and with a short cooking time, so a greatly satifying effort to reward ratio. The quality of the miso does really shine through here. I've already adopted this as part of our repertoire. Thanks again! (Unlikely I'll ever be able to get it to last a week)

EDIT TO UPDATE
I must have made this every other day since this last post. We prefer this to standard dashi based miso shiru. So far I've learnt:
Jerusalem Artichokes really are a fantastic addition to this soup. It's a little lacking without them.
Potatoes are fine, so are pak choi.
Parsnip... not so good. When I ran out of the chokes I thought these might be a good substitute. Somehow, parsnips cancel some of the best flavours out - not recommended.