Cook noodles as package directs. Drain and divide among 4 bowls.
Combine soy sauce, sesame oil, and broth and set aside.
Cut tofu lengthwise into 3 pieces. Cut crosswise into 1/2-in. sticks and pat dry with paper towel.
Heat 1 tablespoons vegetable oil in a large frying pan over high heat. Brown tofu (don’t stir), 4 minutes; brown on other side. Set on noodles.
Add remaining 1 tablespoons vegetable oil to same pan over medium-high heat. Cook ginger and garlic until fragrant, 30 seconds. Add bok choy and cook until wilted, 5 minutes. Add reserved broth mixture and cook until hot, about 1 minute.
Spoon mixture over noodles and tofu and sprinkle with onions sprinkled on top.