I am not sure what the right translation is for this recipe but oden is a one-pot dish, which is a little bit different from stew or hot pot. It's more like a simmered dish: assorted fish balls, fish cakes, atsuage (deep-fried tofu), hard-boiled eggs, konnyaku, and some vegetables are simmered in soy sauce-based broth. I usually make oden a day before so that all the ingredients will absorb good oden broth and it tastes much better the following day. In my house, I usually serve it with onigiri (rice balls). The color seems boring because it's mainly brown, but the flavor is amazing and exquisite. Maybe that's why it's a lot of people's winter comfort dish.
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Note: Here are some brief notes on some of the more obscure ingredients. Usukuchi soy sauce is not the same thing as low-sodium soy sauce. Kikkoman and other well known producers of soy sauce sell usukuchi soy sauce in Japanese grocery stores as well as online. Konnyaku cakes are readymade grayish yam cakes flavored with seaweed powder; they have a mild flavor and a firm, jelly-like texture similar to fish cake; these can also be found online. Nerimono, also known as surimi, are packs of assorted fish cakes in various shapes, colors, and sizes, found in Japanese and Korean grocery stores. Mochi bijin are unsweetened Japanese rice cubes and can be found in Japanese grocery stores or online.
Prepare the dashi stock according to the package directions, preferably using a clay pot. Add the usukuchi soy sauce, regular soy sauce, sake, sugar, mirin, and salt.
Using a paring knife, carefully remove the corners from the daikon so that there are no sharp edges. (This will prevent the daikon from breaking into pieces as it cooks.)
If serving rice, wash the rice, drain, and reserve the water. Cook according to the package directions. Put the daikon and the reserved water in a small pot and boil until a skewer goes through (do not cover with a lid).
Cut the nishime kombu into short pieces (about 6 inches) and quickly rinse the coating under running water. Tie each piece into a basic knot. Cut the octopus into roughly 6-inch pieces and place onto skewers.
Place the konnyaku in a pot of water and bring to a boil. Once it comes to a boil, cook for 1 more minute and drain. Set aside.
Bring a large pot of water to a boil. Add the nerimono and cook for 15-30 seconds. Drain and set aside. Repeat the same process for the aburaage. Once cooled, halve aburaage and the larger nerimono.
Open one side of each aburaage so you can stuff it with mochi. Use a toothpick or kombu to tie the aburaage so the mochi won't fall out during the cooking process. Put the nishime kombu, octopus, konnyaku, eggs, leek, and carrot into a large pot, preferably a clay pot, and cook for 2-3 hours minimum. Skim off the scum and fat along the way. Half an hour before completion, add the nerimono, stuffed aburaage, and daikon.
Cover and reheat when you are ready to serve. (I usually let it all soak for overnight in the refrigerator after it cools down to allow the flavors to meld and serve it the next day.) Serve with rice and karashi, if using.