Whisk the soy sauce, water, sherry, sugar, red pepper flakes, and cornstarch together in a small bowl until the sugar dissolves.

Spread the tofu over a paper towel-lined baking sheet and let drain for 20 minutes. Pat the tofu dry with fresh paper towels, toss with cornstarch in a large bowl, then transfer to a strainer and shake gently to remove any excess powder.

Combine the scallions, garlic, ginger, and a teaspoon of oil in a small bowl. Heat two tablespoons of oil in a 12-inch nonstick skillet over high heat until just smoking, then add the tofu and cook until crisp and well browned on all sides, about 10 to 15 minutes. Transfer the tofu to a bowl.

Add the remaining oil to the skillet and return to high heat until 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 mixture into the pan, until fragrant, about 30 seconds.

Return the tofu to the skillet and stir in the bok choy greens. Whisk the sauce to recombine, then add it to the skillet and cook, stirring constantly, until the sauce has thickened and glossily coats the ingredients, 1 to 2 minutes. Serve hot.