Thick, slippery udon noodles in a simple dashi-based soup are the very definition of comfort food when the weather turns cold.

Two of the most popular everyday hot udon soups are named after animals that have a special place in Japanese folklore and the Shinto religion: the kitsune (fox) and the tanuki (Japanese raccoon dog). Kitsune udon is udon soup topped with a plump square of abura-age (deep-fried flat tofu) that’s been simmered in a salty-sweet broth. Tanuki udon uses the same soup, but is instead topped with tenkasu (also called agedama; tempura batter crumbs), which add flavor and richness to the soup at little cost.

Both kitsune and tanuki udon soups probably debuted sometime in the late Edo Period (1603-1868), although there are conflicting theories that suggest the soups may have been invented later.

Kitsune udon gets its name from its abura-age topping. Abura-age is associated with Inari Okami, the god of agriculture, fertility and prosperity, and is used as the wrapping for inarizushi (deep fried tofu, stuffed with rice). The god is associated with foxes (kitsune) due to their thriftiness — as evidenced by the fox statues at shrines dedicated to Inari Okami such as Fushimi Inari Taisha in Kyoto.

There are several theories for how tanuki udon got its name, but the most popular school of thought is that it is derived from a pun. The topping used for tanuki udon is tenkasu, the leftover bits of fried batter used to make tempura, or in other words batter without the tane or filling — ergo ta(ne) nuki, “without tane.”

The soba noodle versions of each dish are named kitsune soba and tanuki soba respectively. Or at least this is what I’ve always known kitsune and tanuki udon and their soba equivalents to be called as I’m from Tokyo and both my parents are from the Kanto region. But there are regional differences.

In Osaka, udon topped with abura-age is called kitsune or ketsune udon, but soba topped with abura-age is called tanuki soba; kitsune soba and tanuki udon historically didn’t exist at all. There is an equivalent to tanuki udon, with a tenkasu topping, but it’s called haikara udon, not tanuki udon.

And in Kyoto, kitsune or ketsune udon is topped with thinly sliced abura-age instead of the whole pieces that were the norm for me as a child. Those pieces are coated in a clear an sauce that’s thickened with kuzuko (kudzu starch), adding extra flavor to the dish.

However, the popularity of instant-noodle versions of the Kanto style of kitsune and tanuki udon, as well as the dominance of Tokyo-based culture over the rest of the country, has helped to spread the Kanto notions of kitsune and tanuki udon and soba nationwide.

Regardless of what you call them, both hot udon soup versions are quite easy to prepare. The key is the dashi that is the base of the soup; make it from scratch for the best results.

Kitsune udon: Hot udon noodle soup topped with abura-age (flat deep-fried tofu) Ingredients (serves 2): For the dashi: • 10 grams konbu seaweed (a 15-centimeter square piece) • 10 grams katsuobushi (bonito flakes — a large handful) • 1 liter water For the simmered abura-age: • 4 pieces of 7-10 centimeter square abura-age • 400 milliliters dashi • 2 tablespoons soy sauce • 3-4 tablespoons sugar For the udon noodles: • 4 pieces of 7-10 centimeter square aburaage (flat deep-fried tofu) • 600 milliliters dashi • 2 teaspoons soy sauce • ½ teaspoon salt • 2 teaspoons mirin • Chopped Japanese leek or green onions • 2 slices kamaboko (fish cake) — optional • Shichimi tōgarashi (blend of seven spices) Preparation Make the dashi. Wipe off any dirt from the surface of the konbu seaweed using a tightly wrung-out moist kitchen towel. Put it in a pan with the water and soak for at least an hour. Heat the water, and when it has just about come to the boil, add the katsuobushi and turn off the heat. Leave until the katsuobushi has sunk to the bottom of the pan. Strain through a fine mesh sieve. Place the abura-age in a colander. Bring some water to the boil, and pour it over the abura-age to remove the surface oil. Leave until cool enough to handle, then drain. Put 400 milliliters of dashi, soy sauce and sugar in a pan, and add the drained abura-age. Turn the heat to medium. When the liquid is bubbling, turn the heat low, put on an otoshi-buta (drop lid) and simmer for 15 to 20 minutes. Leave the abura-age to cool in the liquid. Cook the udon in boiling water until it’s heated through, then drain. Heat 600 milliliters of dashi with the soy sauce, salt and mirin while the udon cooks. Heat the abura-age in its simmering sauce, then drain. Put the udon into two bowls, ladle in the soup and top with one or two pieces of abura-age and a slice of kamaboko per bowl. Add the green onions and serve with the shichimi tōgarashi on the side. Variation — Tanuki udon: Omit the abura-age, and top the udon soup with some tenkasu (tempura batter crumbs), some blanched komatsuna greens or spinach (optional) and chopped green onions.

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