Preheat the oven to 375 degrees F. Lightly oil a baking sheet and set aside.
Cut the tofu into 1/2-inch slabs and press well to remove any excess water. Cut the slabs into 1/2-inch cubes and toss with 1/4 cup of the soy sauce. Arrange the tofu on the prepared baking sheet and bake for 30 minutes. Remove from the oven and set aside to cool.
In a large bowl, combine the cabbage, carrots, and green onions. Set aside.
In a small bowl, combine the garlic, ginger, sugar, chili paste, remaining 1/4 cup soy sauce, vinegar, oil, and water.
Pour the dressing over the cabbage mixture and toss to combine. Taste and adjust seasonings, if necessary. Let the salad sit for 15 to 20 minutes to allow flavors to develop. Serve topped with tofu.