In a bowl, combine the soy sauce and cornstarch. Add the tofu cubes and gently toss until well coated. Let it marinate for about 10 minutes.
Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat. Add the marinated tofu and cook until golden brown on all sides. Remove the tofu from the skillet and set it aside.
In the same skillet, add the remaining tablespoon of olive oil. Stir in the minced garlic and grated ginger, and cook for about 1 minute until fragrant.
Add the frozen broccoli florets and sliced carrots to the skillet. Cook for 4-5 minutes, stirring occasionally, until the vegetables are tender.
In a small bowl, whisk together the water and sesame oil. Pour the mixture into the skillet and stir to combine.
Return the tofu to the skillet and toss it with the vegetables and sauce. Cook for an additional 2-3 minutes to heat through.
Sprinkle with sesame seeds (optional) and serve the tofu stir-fry hot. It can be enjoyed on its own or served over steamed rice or noodles.