Preheat oven to 400 degrees. Line a large baking sheet with parchment paper.
Drain the tofu and cut it into cubes.
To get more water out of the tofu, press it between two cutting boards. Add a layer of paper towels (or a thin linen) on top and bottom of the tofu. Add a cutting board on top and bottom of the tofu. Add a weight (a book or heavy skillet) onto the top cutting board so that it applies pressure to the tofu. Let it sit for at least 10 minutes (ideally 30 - 40 minutes).
Add the tofu to a large mixing bowl. Drizzle with soy sauce and olive oil. Sprinkle in salt, pepper, and ginger.
Add the cornstarch to the bowl and toss to coat.
Transfer the tofu to the baking sheet, arranging it in one layer.
Bake for 25 - 30 minutes, tossing the tofu after 10 minutes. Bake until the tofu is browned and crispy. For extra crispiness, broil the tofu for 1 - 2 minutes before removing from the oven.