Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Drain the tofu and wrap it in a clean kitchen towel or paper towels; place a heavy skillet on top for 15 minutes to press out excess moisture.
While the tofu presses, wash the potatoes and cut them into 1/2-inch cubes. Trim the tough ends off the broccolini stems.
In a small bowl, whisk together the tamari, toasted sesame oil, maple syrup, grated ginger, and minced garlic to create the marinade.
Cut the pressed tofu into 1-inch cubes and place them in a large mixing bowl along with the potato cubes.
Pour the marinade over the tofu and potatoes, then add the sea salt and black pepper. Toss gently until everything is evenly coated.
Spread the tofu and potatoes in a single layer on the prepared baking sheet, ensuring they are not overcrowded.
Roast in the oven for 20 minutes. Remove the pan and flip the tofu and potatoes with a spatula.
Add the broccolini to the pan, tossing it lightly in any remaining juices on the tray, and roast for another 15 minutes until the potatoes are tender and the tofu is golden.
Serve immediately while the vegetables are crisp and the tofu is warm.