Drain the tofu. Wrap it in a double layer of paper towels and press down lightly to absorb the excess moisture. Cut the tofu into 3⁄4-inch cubes.
In a large nonstick skillet or wok, heat the avocado oil over medium-high heat. When the oil is hot, add the tofu. Drizzle with 1 tablespoon of soy sauce. Sauté, stirring every few minutes or so, until the tofu is browned on most sides, 8 to 10 minutes. Add the garlic, about two-thirds of the green onion, the ginger, red pepper flakes (if using) and the remain- ing 1 tablespoon soy sauce. Stir and cook until fragrant, about 1 minute.
Add the broccoli and cook until crisp-tender, 4 to 6 minutes. Stir in the sesame oil and sprinkle in the sesame seeds (if using). Remove from the heat and garnish with the remaining green onions. Add more soy sauce, if needed.
Notes
For the best texture, remove as much liquid as possible from the tofu before stir-frying. For better removal, the cut tofu cubes can be pressed between paper towels and allowed to sit in the refrigerator for several hours. The paper towels should be changed if soaked.