Heat 1 tablespoon neutral oil in a large pot over medium heat. Add the onion, ginger, and garlic, and sauté for 3 to 4 minutes.
Add the sweet potato and sauté for 1 minute. Season with the dashi granules and sauté for 1 to 2 minutes.
Simmer the soup:
Add the water and cubed tofu to the pot. Bring to a boil. Reduce the heat to low and simmer uncovered for 30 minutes until the sweet potatoes are fork-tender. Taste and add a small pinch of salt if needed.
Cook the udon:
Bring a large pot of water to a boil. Add the frozen udon and cook according to package directions. Drain and divide between four bowls.
Finish the soup:
Add the chopped Napa cabbage to the pot along with ⅓ cup tamari, 1 tablespoon sesame oil, and 1 tablespoon chili oil. Simmer for 5 to 7 minutes until the cabbage wilts. Taste and adjust the seasonings to your preference.
To serve:
Ladle the soup over the cooked udon and serve with sesame seeds or furikake. Enjoy!
Notes
Note 1: 26 ounces is the weight of frozen or fresh udon. If using dry udon (or another dried noodle), use an 8- to 12-ounce package, depending on the manufacturer. Dry noodles will weigh less than their fresh or frozen counterparts.