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Step 1
Drain the tofu and pat very dry with a paper towel, changing the towels a few times as needed. Press on the tofu a little to squeeze some water out, but not so hard you cause it to crumble. Cut the block in half right through the middle (as if you were cutting a burger bun), then cut into 1-inch cubes. Place on a large plate or a rimmed baking sheet and lightly pat dry once more.
Step 2
Sprinkle the cubes slowly and evenly with 2 tablespoons of the cornstarch (I like to scatter on 1/2 tablespoon at a time and toss the cubes halfway through). With your fingers, gently toss to coat the tofu as evenly as you can.
Step 3
In a small mixing bowl or liquid measuring cup, stir together the soy sauce, water, hoisin, rice vinegar, garlic, ginger, and remaining 1 teaspoon cornstarch.
Step 4
In a large nonstick skillet or wok, heat 1 tablespoon oil over medium-high. Once the oil is hot and shimmering, add the broccoli, salt, and pepper. Cook, stirring occasionally, until the broccoli is crisp-tender, about 5 minutes. Remove to a plate and set aside.
Step 5
Add the 2 tablespoons remaining oil over medium-high. Add the tofu in a single layer and cook, tossing every 3 or so minutes, until it is golden on all sides. The tofu may stick together and some bits might crumble a bit. Use a sturdy spoon to break stuck pieces apart and don't worry about any crumbles. They taste extra delicious.
Step 6
Return the broccoli to the pan and pour the sauce over the top. Stir to combine, then let cook until the broccoli is heated through and the sauce has thickened a little, about 1 minute. Stir in the sesame oil and green onion. Sprinkle with sesame seeds. Enjoy hot with rice.