Press tofu for 10 minutes to remove moisture.
Heat vegetable oil in a wok over medium-high heat.
Add tofu cubes and fry until golden brown, about 6 minutes.
Remove tofu and set aside.
In the same wok, add sesame oil, garlic, and ginger; stir 30 seconds.
Add broccoli and carrot; cook for 3–4 minutes until tender but crisp.
In a bowl, whisk soy sauce, vinegar, syrup, cornstarch, and water.
Pour sauce into wok and stir until slightly thickened.
Return tofu to the pan and toss until evenly coated.
Serve warm, topped with sesame seeds or green onions.