Whisk the vegetable broth, soy sauce, rice wine, sugar, cornstarch, and sesame oil in a small bowl until the sugar dissolves.

Spread the tofu cubes on paper towels and pat them dry to remove as much moisture as possible. Toss the dry tofu with the cornstarch in a large bowl until the cubes are thoroughly and evenly coated.

Heat two tablespoons of vegetable oil in a large nonstick skillet over high heat until the oil shimmers. Add the tofu in a single layer and cook until golden brown and crisp on all sides, about 8 to 10 minutes, then transfer to a plate.

Add the remaining vegetable oil to the skillet and return to high heat. Stir in the bok choy stalks and carrots and cook until they are vibrant and just beginning to soften, about 2 to 4 minutes.

Push the vegetables to the edges of the skillet to clear a space in the center. Add the scallions, garlic, and ginger to the center and cook until fragrant, about 30 seconds — keep them moving so they don't burn — then stir them into the rest of the vegetables.

Return the browned tofu to the skillet along with the bok choy greens. Whisk the sauce to recombine the starch, then pour it into the skillet and toss everything together until the sauce is thickened, glossy, and clinging to the tofu, about 1 minute.

Serve hot with steamed rice.