Heat 1 tablespoon of the sesame oil in a large skillet over medium-high heat. Add the cubed tofu and cook for 6 to 8 minutes, turning occasionally until the edges turn golden.
Add the broccoli florets and sliced carrots to the skillet. Stir and cook for 4 to 5 minutes until the vegetables are bright and still crisp.
In a small bowl, stir together the soy sauce, grated ginger, minced garlic, and remaining tablespoon of sesame oil. Pour the sauce over the tofu and vegetables.
Toss everything to coat evenly and cook for 1 to 2 minutes more until the sauce thickens slightly.
Divide the cooked rice among four bowls. Spoon the tofu and vegetable mixture on top. Finish with sesame seeds and sliced green onions.