Heat the oil in a medium pot over medium heat.
Sauté the onion until translucent, 3 to 4 minutes.
Stir in the garlic and ginger and cook 30 seconds until fragrant.
Toast the gochugaru and gochujang in the pot, stirring for 1 minute.
Add the kimchi and daikon and cook 3 minutes to soften slightly.
Pour in the kimchi brine and broth and bring to a boil.
Season with soy sauce and sugar, then reduce to a gentle simmer.
Simmer 12 to 15 minutes, until the daikon is tender.
Slide in the mushrooms and tofu and simmer 5 minutes more.
Finish with sesame oil and most of the scallions. Taste, then add salt and pepper.
Ladle into bowls and garnish with the remaining scallions. Serve hot.