Make the sauce: In a bowl or shallow dish, combine hoisin sauce, tamari (or soy sauce), minced garlic, grated ginger (if using), and toasted sesame oil; stir until smooth.
Prepare the tofu: Cut the pressed extra-firm tofu into bite-size cubes (about 3/4-inch or to your preference).
Marinate: Add the tofu cubes to the sauce and gently toss to coat. Let sit for about 10 minutes to absorb flavor.
Heat the skillet: Warm the toasted sesame oil in a large skillet over medium heat until shimmering.
Cook the tofu: Add the marinated tofu and any remaining sauce to the skillet, spreading the cubes into a single layer. Cook without stirring for 5–6 minutes until the bottoms are lightly seared.
Add green onions and finish cooking: Slice the green onions while the tofu sears. Reduce heat to medium-low, add the green onions, then stir and cook 2–3 more minutes until the tofu reaches your desired texture.
Serve: Serve warm over rice, quinoa, or noodles with vegetables as desired, and optionally garnish with sesame seeds or red pepper flakes.