Bring a large pot of water to a boil and cook the soba noodles according to package directions. Drain, rinse under cold water, and set aside in a large mixing bowl.
Toss the tofu cubes with cornstarch until evenly coated. Heat the vegetable oil in a skillet over medium-high heat and cook the tofu for 8 to 10 minutes, turning occasionally, until golden and crisp on all sides. Remove from the skillet and set aside.
In a small bowl, whisk together the peanut butter, soy sauce, lime juice, sesame oil, garlic, ginger, and water until smooth.
Add the sliced bell peppers to the bowl of cooled noodles. Pour the peanut sauce over the top and toss gently until everything is coated.
Top the salad with the crispy tofu cubes, then sprinkle with green onions, cilantro, and chopped peanuts just before serving.