Using kitchen scissors, carefully open the tofu package. Drain the liquid. Place the tofu between 2 plates. Weight the top plate with a heavy jar for 20 minutes. Remove the tofu from the plates, draining and discarding the liquid.
Cut tofu into 1-inch cubes. Combine vegetable oil, tamari, garlic, and grated ginger in a bowl. Add tofu and marinate at room temperature for at least 30 minutes, turning tofu occasionally.
Place tofu and marinade in a shallow baking dish. Bake for 50 to 60 minutes at 350ᵒ F. Turn tofu cubes several times during baking. Cooking is complete when tofu is firm and nicely browned.