Warning: Mixing wasabi and karashi paste may cause an explosion. Only a joke of course, but I’ve gotten a few laughs out of that.
Karashi is a mixture of ground mustard seeds and horseradish – like wasabi- a little goes a long way. So unlike European mustard, it’s not an emulsion based with vinegar. It’s normally sold in a dried powder form (just add water), or as a paste in a tube.
Karashi paste is served as a condiment with dishes such as tonkatsu, steak and oden. It is also used in sauces based with miso, mayonaise and sometimes in sunomono (things with vinegar) dressing.

Where can I buy the Karashi Hot mustard in the southern Califronia market?
You should be able to find it at most Asian grocery stores. Of course, a Japanese grocery store would have it. If that’s not available look for Korean and or perhaps even a Chinese specialty grocery store. Of course you can find it online - http://www.amazon.com/Karashi-hot-mustard-tube-1-52/dp/B0002YEXWA
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