This is a speciality dish of the Sanuki region (in Kagawa prefecture on Shikoku, Japan). My mother used to make this for me on New Year's Eve. The vegetable stock is very warming. I highly recommend this recipe.
Finely julienne the carrot. Quarter the daikon radish and slice. Bring the dashi stock to a boil, and simmer the vegetables over medium heat for about 15 minutes until tender.
Pour boiling water over the aburaage to get rid of the excess oil on the surface. Cut into thin strips and add the the pot with the dashi and vegetables. Simmer for another 15 minutes over medium heat.
Add the soy sauce and adjust the seasoning. Turn off the heat, and let rest for about 2 hours.
Boil the udon noodles and drain well.
Transfer the udon noodles to serving bowls. Warm up the soup and ladle into the bowls. Top with green onion and it's done.
Story Behind this Recipe
This is a traditional regional speciality of the Sanuki region, in Kagawa prefecture. You don't see it often listed on the menus of udon restaurants, but it's a very popular homemade dish, especially on New Year's Eve where it's eaten as "toshikoshi udon" (year-end udon) instead of the usual toshikoshi soba. The vegetable stock really warms you up.
The dashi (stock) that comes out of the daikon radish and carrot should blend well with the flavor of the aburaage (fried tofu). Let the soup rest for about 2 hours after adding the soy sauce so that the flavors of the soy sauce and dashi can really blend together.