Cut the tofu into 8 slabs crosswise. Blot well on paper towels or clean tea towels (or use a tofu press like the handy Tofu XPress ahead of time for making the tofu nice and firm). Cut the slabs into 2 equal squares, and each square into 2 triangles.
Combine the soy sauce, oil, and sugar in a wide skillet. Before they get too hot, add the tofu. Stir quickly to coat, then sauté over medium-high heat, stirring occasionally, until the tofu turns golden and crisp on most sides. Remove the tofu to a plate and set aside.
Combine the green vegetables, mushrooms, and optional baby cornin the same skillet. Add just enough water to keep the skillet moist. Cover and steam over medium heat until the vegetables are just barely tender-crisp and still bright green.
Drain any liquid that remains in the skillet, then gently stir in the tofu. Stir in the sauce of your choice as noted in the first ingredient in the list.
Spice the dish up with ginger, red pepper flakes, and/or ginger, if you'd like. Serve at once with the sauce of your choice.