Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Drain the tofu and wrap it in a clean kitchen towel or paper towels; place a heavy object on top and press for 15 minutes to remove excess moisture.
Cut the pressed tofu into 1-inch cubes and place them in a bowl.
Toss the tofu cubes with sesame oil, sea salt, and black pepper until evenly coated.
Spread the tofu in a single layer on the prepared baking sheet and bake for 25-30 minutes, flipping halfway through, until the edges are golden and crispy.
While the tofu bakes, whisk together the peanut butter, tamari, lime juice, grated fresh ginger, minced garlic, and sriracha in a small bowl until smooth.
Steam the broccoli florets and shelled edamame for 5-6 minutes until they are tender-crisp and bright green.
Remove the tofu from the oven, transfer to a bowl, and gently toss with the peanut sauce until well coated.
Serve the crispy peanut tofu immediately alongside the steamed broccoli and edamame.