To make the dashi stock, soak the kombu in a pot with water for 10 minutes. After that, turn on the heat and wait until just starting to boil. Remove from heat and add the katsuobushi. Wait for 3-4 minutes and pour the stock through a strainer discarding the solids.
In a skillet, add the sesame oil and spread the sweet potato cubes in a single layer. Cook for 1 minute, then shake the skillet to flip them and cook for a minute more. Set aside.
In a 2-quart pot, bring the stock to a rolling boil. Reduce the heat to a simmer and add the daikon, carrot, and salt. Simmer for 2 minutes or until the veggies are barely tender. Skim away any froth if it appears.
Add the shiitake mushrooms. Cook for 3-4 minutes. Add the soy sauce and mirin. Add the sweet potato cubes.
Mix the cornstarch with water to get a paste and stir it into the soup, on a high heat. Continue stirring for about a minute, until the soup thickens. Sprinkle with the chopped green onions and serve. Enjoy!
Adapted from Washoku: Recipes from the Japanese Home Kitchen by Elizabeth Andoh