Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Press the extra firm tofu for at least 15 minutes to remove excess moisture, then cut it into uniform 1-inch cubes.
In a medium mixing bowl, toss the tofu cubes with arrowroot powder, garlic powder, ginger powder, sea salt, and black pepper until each piece is evenly coated.
Spread the coated tofu, broccoli florets, and shelled edamame onto the prepared baking sheet in a single layer.
Drizzle the sesame oil and tamari over the tofu and vegetables, tossing gently with your hands or a spatula to ensure a light, even coating.
Roast for 25-30 minutes, flipping the tofu halfway through the cooking time, until the tofu is golden-brown and the broccoli has developed charred, crispy edges.
Remove the tray from the oven and sprinkle the toasted sesame seeds over the top before serving warm.