Remove the tofu from its package, wrap the whole block in a clean absorbent kitchen towel or several layers of paper towel, place it on a plate, and set a heavy, sturdy item on top to press out moisture. Press for at least 10 minutes (longer is better). While the tofu presses, preheat your oven to 425°F.
After pressing, unwrap the tofu and cut it into cubes.
Heat 2 tablespoons of the cooking oil in a cast-iron skillet over medium-high heat. Add the tofu cubes and sprinkle with the ½ teaspoon salt. Cook, turning occasionally, until all sides are golden and beginning to crisp, about 5–7 minutes total.
Transfer the skillet to the preheated oven and bake the tofu for 15 minutes, until crispy. (If your skillet is not oven-safe, transfer the tofu to an ovenproof baking dish before baking.) Remove the skillet from the oven and set the tofu aside.
While the tofu bakes, bring a pot of water to a boil. Add the broccoli florets and blanch for 1 minute. Drain the broccoli and set aside.
Make the sauce: in a bowl combine ¼ cup white vinegar, ¼ cup water with the 1 teaspoon veggie bouillon paste dissolved into it, 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 the bouillon paste and arrowroot powder are fully dissolved and the mixture is smooth.
Return the same skillet to medium heat and add the remaining 1 tablespoon cooking oil. Add the minced garlic (4 cloves), minced or grated fresh ginger (1 tablespoon), and the finely chopped white and light green parts of the green onions. Sauté until fragrant, about 30 seconds to 1 minute.
Add the blanched broccoli to the skillet and cook, stirring, for 3–5 minutes until the broccoli is heated through and slightly tender.
Stir the sauce once more, pour it into the skillet with the broccoli, and cook while stirring until the sauce thickens and coats the broccoli, about 1–2 minutes.
Add the baked tofu back to the skillet and gently toss to coat and warm through, about 1–2 minutes.
Serve the broccoli and crispy tofu over the 2 cups cooked brown rice.