Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Press the tofu between paper towels for 10 minutes to remove excess moisture, then cut into 1-inch cubes.
In a mixing bowl, toss the tofu cubes with cornstarch, sea salt, and black pepper until evenly coated.
Spread the tofu on the prepared baking sheet and drizzle with sesame oil. Bake for 25-30 minutes, flipping halfway through, until golden and crispy.
While the tofu bakes, whisk together the peanut butter, tamari, rice vinegar, and grated ginger in a small bowl. If the sauce is too thick, add a teaspoon of warm water.
Steam the broccoli florets and edamame for 5 minutes until tender-crisp.
Toss the crispy tofu in the peanut sauce until well coated.
Serve the peanut tofu over the steamed vegetables and garnish with sesame seeds.