Remove the tofu from its package, wrap the whole block in an absorbent kitchen towel or several layers of paper towel, place on a plate, and put a heavy item on top to press out moisture. Press for at least 10 minutes. While the tofu presses, preheat the oven to 425°F (220°C).
Meanwhile, prepare the other ingredients: cut the 2 crowns of broccoli into florets; mince 4 cloves garlic; mince or grate 1 tablespoon ginger; finely chop the white and light green parts of 1 bunch of green onions; measure out the remaining ingredients and have 2 cups cooked brown rice ready.
After pressing, unwrap the tofu, pat it dry with a towel, and cut it into cubes.
Heat 2 tablespoons cooking oil in a cast iron skillet over medium-high heat. Add the tofu cubes and ½ teaspoon salt. Cook, turning occasionally, until all sides are golden and beginning to crisp, about 5–7 minutes.
Transfer the skillet to the preheated oven and bake the tofu for 15 minutes, until crispy. Remove the skillet from the oven and transfer the tofu to a plate; set aside.
In a bowl, make the stir-fry sauce: combine ¼ cup white vinegar, ¼ cup water plus 1 teaspoon veggie bouillon paste (stir to dissolve), 2 tablespoons soy sauce, 2 tablespoons fermented black bean sauce, 1 tablespoon sugar, 1 tablespoon toasted sesame oil, and ½ tablespoon arrowroot powder. Whisk until smooth and the arrowroot is dissolved; set aside.
Return the skillet to the stove over medium heat and add the remaining 1 tablespoon cooking oil. Add the minced garlic, minced ginger, and chopped green onions (white and light green parts) and sauté, stirring, until fragrant, about 30–60 seconds.
Add the broccoli florets to the skillet and cook, stirring occasionally, until bright green and tender-crisp, about 4–5 minutes.
Give the sauce a quick stir, pour it into the skillet with the broccoli, and stir constantly as the mixture comes to a simmer. Cook until the sauce thickens and coats the broccoli, about 1–2 minutes.
Return the baked tofu to the skillet and gently toss or stir to coat the tofu with the sauce and heat through, about 1–2 minutes.
Serve the broccoli and crispy tofu over the 2 cups cooked brown rice immediately.