Whisk the sauce ingredients together in a small bowl until the sugar and cornstarch are fully dissolved.

Spread the tofu out over a paper towel-lined baking sheet and let it drain for 20 minutes to remove excess surface moisture. Pat the tofu dry with paper towels, then toss it with cornstarch in a large bowl until evenly coated. Transfer the tofu to a strainer and shake it gently to remove any excess cornstarch so the coating remains light and crisp.

Combine the scallions, garlic, ginger, and one teaspoon of oil in a small bowl. Heat two tablespoons of oil in a 12-inch nonstick skillet over high heat until the oil just begins to smoke. Add the tofu and cook until every side is golden-brown and crisp, about 10 to 15 minutes, then transfer the tofu to a clean bowl.

Add the remaining oil to the same skillet and return to high heat until the oil is shimmering. Add the bok choy stalks and carrots and cook until the vegetables are crisp-tender, about 4 minutes. Clear the center of the skillet, add the garlic-ginger mixture, and cook, mashing the aromatics into the pan until fragrant, about 30 seconds. Stir the aromatic mixture into the surrounding vegetables.

Return the fried tofu to the skillet and add the bok choy greens. Whisk the sauce once more to recombine, then pour it into the skillet. Cook, stirring constantly, until the greens wilt and the sauce has thickened into a glossy glaze, about 1 to 2 minutes. Serve hot over rice.