Prepare the daikon radish: Peel the daikon and cut into 2-3 cm thick rounds. Score a crosshatch pattern on one side of each round to help it absorb flavor. Par-boil the daikon in water for about 10 minutes, then drain and set aside.
Prepare other ingredients: Score the konnyaku into crosshatch patterns and cut into triangles or rectangles. Blanch konnyaku in boiling water for a few minutes to remove the smell, then drain. Briefly blanch atsuage and other fried fish cakes in hot water to remove excess oil. Peel the hard-boiled eggs. Peel potatoes and cut into halves if large.
Make the dashi broth: In a large pot, combine water and kombu. Heat over medium heat until it almost boils. Remove kombu just before it boils. Add katsuobushi and immediately turn off the heat. Let it steep for 5 minutes, then strain the dashi through a fine-mesh sieve, discarding the solids.
Return the strained dashi to the pot. Add soy sauce, mirin, sake, sugar, and salt. Bring to a gentle simmer over medium heat.
Add the daikon radish and potatoes to the simmering broth. Simmer for about 30 minutes until they are tender.
Add the konnyaku, hard-boiled eggs, atsuage, ganmodoki, and chikuwa to the pot. Continue to simmer for another 30-60 minutes, or until all ingredients are thoroughly heated through and have absorbed the flavors of the broth.
Finally, add the satsuma-age and mochi kinchaku (if using) and simmer for another 10-15 minutes, as these cook faster.
Serve hot. Oden tastes even better the next day as the flavors deepen.
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