The umami-rich oden broth will improve whatever ingredients you add to it. (Edward Schneider for The Washington Post)

During our October trip to Japan, my wife, Jackie, and I had dinner at a restaurant specializing in oden, which is essentially vegetables and many other things simmered in a flavorful broth, ideally eaten in cold weather.

This was a lively neighborhood place in Kanazawa, with a few tables and a counter, behind which the two engaging women who run the restaurant dish up whatever the customer asks for. And that’s the trick to ordering: It doesn’t matter what you select. Just pick things you like, or think you might like.

How do you do this if you don’t speak Japanese and don’t have someone with you who does? That’s the beauty of sitting at the counter: You just point. We had daikon, fish balls, eggplant, potatoes and tofu. (The guy on the stool next to Jackie had supplied the tofu to the restaurant, so how could we fail to get some?) We had beef tendon. We had a bowl of rice. We drank beer. It was great fun, and it was delicious.

For one thing, the produce was excellent. But what makes oden oden is the cooking liquid, and it turns out to be easy, if not to duplicate, then at least to emulate at home. It is quick enough and simple enough that you don’t need to worry about having a dozen ingredients to make the kind of varied oden that you see in a Japanese restaurant (or a convenience store and similar shops in Japan, which have a vat of oden steaming in the prepared food section). All you need is a few basics, plus some vegetables and maybe a little fish or shrimp, though all-vegetable oden is classic.

One recent evening when the temperature had finally dipped into the 30s, we thought it was time to make our home version of oden. In the fridge were two bunches of medium-size turnips (less than two inches across) and some excellent (and huge) carrots; in the freezer were shrimp. Among the pantry items were dried kombu seaweed (worth keeping in the house for making light “instant” broths), Chinese dried shrimp, soy sauce and sake. That was all I needed.

To make the cooking liquid (which can be done in advance), I put a piece of dried kombu (perhaps 9 by 4 inches) into a saucepan with three cups cold water and five or six dried shrimp. Bonito flakes are the proper dried seafood for this, but dried shrimp are a pretty good substitute. I brought it slowly to the boil, let it barely bubble for a few seconds, then removed the kombu. The shrimp I left to steep as the liquid cooled, then fished them out. To this basic dashi, I added a scant tablespoon of sugar (light brown is nice, but white is fine) and 1 1/2 tablespoons each of sake and soy sauce. If you happen to have any decent mirin in the house (most of what you see in grocery stores is dreadful), add some of that and eliminate the sugar.

I then peeled the turnips and carrots, cut the latter into turnip-size chunks and turned my attention to making shrimp balls. For eight of them, I pureed 1/4 pound of shelled shrimp (not dried shrimp) in a food processor, scraping down the work bowl several times. I then added half an egg, two teaspoons each of flour and cornstarch and a 1/4 teaspoon of fine salt, continuing to process the mixture until it was smooth and glossy. With damp hands, I formed the mixture into one-inch spheres, which I fried for three minutes in a neutral oil at 340 degrees, until just pale golden. (You could do the same with white-fleshed fish such as sole or whiting, but I like the flavor of shrimp for these things.)

I brought the broth back up to a gentle boil and added all the ingredients, including the fried shrimp balls, along with a strip of lemon zest (optional, but it adds aroma). I let it bubble gently for 30 minutes, then left it alone until we were ready to eat, when I reheated the broth and let it simmer for another few minutes. By that time, I’d made some plain rice.

As you’ll see when you make it, the broth gains a great deal from those dried and fermented elements — the kombu, soy sauce and sake all add layers of subtle-but-distinctive flavor. And with a half hour of simmering, this flavor penetrates to the core of porous vegetables such as turnips and does a lot for the carrots and shrimp balls. The reverse is true as well: The broth gets better by the minute, and leftover broth can be frozen and reused.

If I’d been making this for more than two people, I’d certainly have added potatoes, tofu and maybe a couple of hard-cooked eggs. Perhaps daikon, too, though I find it rather dull — except when given the chance to absorb flavor in an oden bath.

Boiling the same ingredients in plain salted water wouldn’t be very enticing on a cold day, but when the temperature drops to the freezing point, oden is really something to look forward to.

Schneider’s Cooking Off the Cuff appears Fridays in All We Can Eat. Follow him on Twitter @TimeToCook.