Prepare the Pork: Heat sesame oil in a large pot over medium heat. Add the sliced pork belly and cook until lightly browned, about 3-4 minutes. Stir occasionally.
Add the Vegetables: Add the sliced carrot, daikon, and onion to the pot. Stir and cook for another 5 minutes, letting the vegetables soften slightly.
Simmer the Broth: Pour in the water and bring the mixture to a boil. Once boiling, reduce the heat to a simmer and cook for 10-15 minutes until the vegetables are tender.
Add the Miso: In a small bowl, mix the miso paste with a bit of the hot broth to create a smooth mixture. Add this to the pot and stir well to combine. Taste and adjust with more miso or soy sauce as needed.
Finish the Soup: Add the shiitake mushrooms and tofu (if using) to the pot. Simmer for an additional 5 minutes. Once everything is cooked through, serve hot, garnished with chopped scallions.