Preheat oven to 400°F and line a large baking sheet with parchment paper.
Press the tofu for 15 minutes using a tofu press or heavy skillet to remove excess moisture, then cut into 1-inch cubes.
In a bowl, toss the tofu cubes with cornstarch, sea salt, and black pepper until each piece is evenly coated.
Arrange the tofu in a single layer on the 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, rice vinegar, sesame oil, maple syrup, grated ginger, and minced garlic in a small bowl.
Steam the broccoli florets for 5-6 minutes until they are tender-crisp and bright green.
Transfer the hot, crispy tofu to a bowl, pour the peanut sauce over it, and toss gently to coat before serving with the broccoli and a sprinkle of sesame seeds.