1. Cook noodles according to package directions. Drain and divide among 4 large bowls.
2. Put broth, dashi powder, mirin, and ginger in an 8-qt. pot and bring to a boil over high heat. Reduce heat to a simmer; add carrots, 1/2 cup green onion, and the tofu. Cook until tofu is heated through, about 3 minutes. Add cabbage and bean sprouts and cook until just wilted, about 2 minutes. Divide among the bowls and garnish with green onion.
*Find fresh udon in refrigerated section, and dashi (Japanese soup stock) powder and mirin in Asian-foods aisle of most grocery stores.