Prepare the kiriboshi daikon: Quickly rinse 2 ounces kiriboshi daikon to remove any surface dirt. Add just enough water to cover the kiriboshi daikon and soak for 15 minutes (see note 1).
Prepare the other ingredients: Meanwhile, peel and julienne 2 small carrots. Cut 5 ounces sliced pork into 1-inch strips.
Drain and cut the kiriboshi daikon: After soaking, measure and set aside the soaking water. Squeeze out the excess water from the kiriboshi daikon with your hands. If the pieces are long, cut them into 2–3-inch strips.
Saute the kiriboshi daikon and carrots: Heat a medium pot over medium heat. Add oil, then stir-fry the kiriboshi daikon and carrots for 1–2 minutes to remove excess moisture from the kiriboshi daikon.
Simmer with pork and broth: Add the sliced pork, ½ cup dashi, ½ cup reserved water from soaking kiriboshi daikon, 2 tablespoons soy sauce, 2 tablespoons mirin, 1 teaspoon sugar, and ⅛ teaspoon kosher salt to the pot, mixing well. Place an otoshibuta (drop lid) on top if you have one, and simmer for about 10 minutes.
Serve and enjoy: Serve warm, chilled, or at room temperature (see note 2).