Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Drain the tofu and press it firmly between paper towels to remove as much moisture as possible, then cut into 1-inch cubes.
In a large bowl, toss the tofu cubes and broccoli florets with the toasted sesame oil until evenly coated.
Spread the tofu and broccoli in a single layer on the prepared baking sheet and roast for 20-25 minutes, flipping halfway through, until the tofu is golden and the broccoli is tender.
While the vegetables roast, bring a pot of water to a boil and cook the soba noodles for 4-5 minutes, then drain and rinse under cold water to prevent sticking.
In a small mixing bowl, whisk together the peanut butter, tamari, lime juice, grated ginger, minced garlic, and red pepper flakes until the sauce is smooth and creamy.
Place the cooked noodles, roasted tofu, broccoli, and shelled edamame into a large serving bowl.
Pour the peanut sauce over the noodle mixture and toss thoroughly to ensure every ingredient is well-coated before serving.