Prepare the ingredients: thinly slice the Carrot and the Shiitake Mushroom, finely chop the Negi and the Mitsuba, and lightly beat the Eggs in a small bowl. Rinse any clumps from the Cooked Japanese Short-Grain Rice so the grains separate easily.
In a medium pot, combine the Dashi with Sake, Mirin, and Soy Sauce. Bring gently to a simmer over medium heat to marry the flavors.
Add the sliced carrot and shiitake to the simmering broth and cook until the vegetables are just tender, about 5–7 minutes.
Stir in the cooked rice, breaking up any lumps, and let it simmer so the rice absorbs the broth and the mixture thickens slightly—about 3–4 minutes. Taste and adjust seasoning with a pinch of Salt or a little more soy sauce if needed.
Reduce the heat to low. Slowly drizzle the beaten eggs into the pot in a thin stream while stirring gently in one direction so the eggs set into soft ribbons rather than a solid mass.
Turn off the heat when the eggs are just set but still silky. Stir in most of the chopped negi and reserve a little for garnish.
Ladle the zōsui into bowls, finish with the remaining negi and the chopped mitsuba for brightness, and serve immediately while hot.
