Press the tofu. Wrap the block in a clean towel and set something heavy on top for 15–20 minutes. This helps remove excess water so it crisps up nicely.
Mix the sauce. In a small bowl, whisk soy sauce, water, brown sugar, vinegar, mirin, garlic, ginger, and red pepper flakes. In a separate cup, stir together cornstarch and water.
Set both aside.
Prep the tofu. Cut pressed tofu into 1-inch cubes. Pat dry. If you want extra crisp edges, sprinkle with 1–2 teaspoons cornstarch and a pinch of salt.
Sear the tofu. Heat 1 tablespoon neutral oil in a large skillet over medium-high.
Add tofu in a single layer and cook 6–8 minutes, turning occasionally, until golden and crisp on most sides. Transfer to a plate.
Cook the broccoli. In the same pan, add another 1 tablespoon neutral oil. Add broccoli and a splash of water.
Cover and steam-sauté 3–4 minutes until bright green and tender-crisp.
Thicken the sauce. Reduce heat to medium. Pour the teriyaki mixture into the skillet with the broccoli. Stir, then add the cornstarch slurry.
Cook 1–2 minutes, stirring, until the sauce turns glossy and thick.
Toss everything together. Return tofu to the pan. Add toasted sesame oil and gently fold to coat. Cook another minute so the tofu absorbs some sauce.
Serve. Spoon over warm rice or noodles.
Top with green onions and sesame seeds. Taste and adjust with a squeeze of lime or a splash more soy if needed.