Lay tofu cubes onto several layers of paper towel; top with more paper towel. Place something heavy onto the tofu to squeeze excess water from the tofu; let sit until the tofu is drained, 20 to 30 minutes.

Preheat oven to 350 degrees F (175 degrees C). Lightly grease a baking sheet.

Heat a small skillet over medium heat. Toast sesame seeds in hot skillet until fragrant, about 5 minutes.

Mix soy sauce, ginger, and sesame seeds together in a large pan. Marinate tofu in the soy sauce mixture until it absorbs some of the sauce, about 12 minutes per side.

Spread marinated tofu onto the prepared baking sheet.

Bake tofu in preheated oven for 15 minutes, flip, and continue baking until firm and heated through, about 15 minutes more.