Bring a medium saucepan of salted water to a boil. Pat the tofu dry between 2 layers of paper towels; season with salt and pepper. Heat 2 tablespoons vegetable oil in a large nonstick skillet over medium heat. Add the tofu and cook, turning once, until well browned and slightly crisp, about 15 minutes; transfer to a plate.
Meanwhile, cook the pasta in the boiling water, 1 to 2 minutes less than the label directs for al dente. Reserve 1 cup cooking water, then drain. Mix the soy sauce, oyster sauce and 1/2 cup of the cooking water in a small bowl.
Add the remaining 1 tablespoon vegetable oil to the skillet. Increase the heat to high and add the broccoli. Cook, stirring, until crisp-tender, about 5 minutes. Add the bell pepper, carrot, jalapeno and ginger and cook until just softened, 2 more minutes. Add the noodles, tofu and soy sauce mixture and cook, tossing, until most of the sauce is absorbed, about 2 minutes. Stir in enough of the remaining 1/2 cup cooking water to loosen. Drizzle with the sesame oil, season with salt and toss.