Press the tofu for at least 15 minutes to remove excess moisture. Cut the pressed tofu into 1-inch cubes.
Preheat the oven to 400°F. Toss the tofu cubes with cornstarch until evenly coated. Drizzle a small amount of sesame oil over them if desired for extra crisping.
Place the tofu on a baking sheet lined with parchment paper and bake for 25-30 minutes, flipping halfway through, until golden and crispy.
Meanwhile, cut the broccoli into florets. Toss broccoli with a drizzle of sesame oil, a pinch of garlic powder, salt, and pepper. Spread on a separate baking sheet and roast in the oven for 20 minutes, or until tender and slightly charred.
In a small bowl, whisk together the natural peanut butter, soy sauce, maple syrup, rice vinegar, and a little water to thin the sauce to your desired consistency.
Once the tofu is crispy and the broccoli is roasted, drizzle the peanut sauce over the tofu, tossing gently to coat evenly.
Plate the crispy peanut tofu alongside the roasted broccoli. Garnish with a sprinkle of extra garlic powder or sesame seeds if desired, and serve warm.