Heat oil in a large saucepan over high. Cook white and pale-green parts of scallions, garlic, and ginger, stirring often, until softened and fragrant, about 3 minutes. Add broth (optional: then whisk in gochujang and soy sauce). Add daikon and gently simmer until daikon is tender, 15–20 minutes.
Add kimchi and tofu. Simmer until tofu is heated through. Carefully divide among bowls. Thinly slice reserved scallion tops and scatter over.
