Slice the tofu in half vertically and press each slab with a towel to remove excess water. Slice crosswise into 1/3- to 1/2-inch (1 cm) squares and arrange them on a cutting board. Cover with a towel and a heavy cookbook to press, then slice the aromatics.
Remove the towel and dab the tofu squares dry if they still appear wet. Season the top of each square with a pinch of salt.
Heat neutral oil in a 12-inch nonstick frying pan over medium-high heat for 2 minutes. Line a cutting board with paper towels while the oil heats.
Carefully add the tofu to the hot oil in a single layer using a slotted spoon. Cook for 5 to 8 minutes until golden brown on the bottom, then flip and cook for another 4 to 5 minutes. Transfer the crisp tofu to the towel-lined board and season with salt.
Whisk the braising liquid ingredients together in a bowl or combine them in a sealed jar and shake well.
Wipe the excess oil from the pan, add chile oil, and heat over medium-high. Sauté the scallion whites, garlic, and ginger for 1 to 2 minutes until fragrant. Add the vegetables and stir-fry for 2 minutes until crisp-tender.
Pour the braising liquid into the pan, bring to a boil, and simmer for 5 minutes until slightly thickened.
Whisk the cornstarch into 1/2 cup (120 mL) of water to create a slurry. Stir the slurry into the pan and whisk for 45 to 60 seconds until the sauce thickens further.
Fold the fried tofu into the sauce to coat. Simmer over medium heat for 10 minutes, stirring occasionally, until the sauce reduces and sticks to the tofu. Remove from the heat and let cool for a few minutes.
Serve the tofu over rice and garnish with sliced scallion greens, sesame seeds, and a drizzle of toasted sesame oil.
