Crack 2 eggs into a bowl and whisk until combined. Mix 2 tsp potato starch (katakuriko) and 2 tsp water in a small separate bowl to make a slurry, set them both by the stove for later.Trim only the hard tip off the stems of 5 fresh shiitake mushrooms, then tear the caps and stems into large pieces. Cut ½ carrot into 5cm (2") matchsticks.
Heat a pot over medium with 1 tsp cooking oil. Add the shiitake and carrots and sauté for about a minute, or until the shiitake are starting to soften and brown at the edges.
Pour in 500 ml dashi stock, 1 tsp Chinese-style chicken bouillon powder, and ½ tsp salt. Stir and bring to a boil, then let it bubble gently for 1½ to 2 minutes.
Stir in 1 tsp Japanese soy sauce (koikuchi shoyu) and taste the broth. Add more salt or soy sauce if needed. Reduce the heat, then mix the slurry again and pour it around the pot. Stir the contents of the pot and bring the heat back up, letting it bubble for 30 seconds to 1 minute.
Pour the whisked egg into the pot in two to three additions. With each addition, leave the egg to form a sheet on top, then gently stir it into the broth before the next addition.
Once the last sheet of egg has formed, turn off the heat and divide into serving bowls. Top with a drizzle of toasted sesame oil and a small heap of finely chopped green onions. Enjoy!
Notes
Tear the shiitake by hand: The test batch I cut with a knife was just another egg soup. Torn into large pieces and sautéed first, the shiitake take center stage.Keep the stems: Only the dark, hard tip at the very base has to go. The rest of the stem is good to eat, and tearing it lengthwise leaves it with a real chew.The thickened broth cradles the egg: Do not skip the potato starch or cut back on it. The thickness holds up the beaten egg, which fans out and firms up slowly while the broth around it stays clear.Settle the salt before thickening: Once the slurry is in, add no more salt or soy sauce. The one thing left to add for flavor is the fragrance of the sesame oil.