Wrap the extra firm tofu in a clean kitchen towel and place a heavy object on top for 15 minutes to remove excess moisture.
Cut the pressed tofu into 1-inch cubes and season evenly with sea salt and black pepper.
In a small bowl, whisk together the tamari, grated fresh ginger, and minced garlic to create the stir-fry sauce.
Heat the toasted sesame oil in a large non-stick skillet or wok over medium-high heat.
Add the tofu cubes to the skillet in a single layer and sear until golden brown and crispy on all sides, about 8-10 minutes.
Remove the tofu from the pan and set aside, then add the broccoli florets and sliced red bell pepper to the same skillet with a splash of water.
Sauté the vegetables for 3-4 minutes until tender-crisp, then return the tofu to the pan along with the shelled edamame.
Pour the tamari mixture over the tofu and vegetables, tossing constantly for 1-2 minutes until the sauce coats everything evenly.
Plate the stir-fry and garnish with sesame seeds before serving.