Stir the sauce ingredients together in a small bowl or container. Set this aside.
Coat the bottom of a large wok with one tablespoon of the oil and place it over medium heat (Note1). Give the oil a minute to heat up, then add the tofu cubes in a single layer (Note 2). Cook the tofu for about 10 minutes, flipping the pieces once or twice, until they're browned and crispy. Transfer them to a plate when done.
Add the remaining oil to the wok and turn up the heat to medium-high. Once the oil is hot, add the green beans. Stir-fry the beans for about 6 to 8 minutes, until they are tender-crisp, bright green, and blistered in spots. Stop stirring every now and then, giving the beans 20 seconds or so to sizzle in the oil. (See Note 3 regarding precautions.)
Turn the heat down to medium. Give the wok a few moments to cool down (Note 4), then push the green beans to the side and add the minced garlic. Sauté the garlic for about 30 seconds.
Stir the garlic and the green beans together. Raise the heat back to medium-high. Return the cooked tofu to the wok, then pour the sauce over the tofu and beans. Continue stir-frying everything for about a minute, until the sauce has thickened and coats the tofu and beans.
Remove the wok from heat and sprinkle the stir-fry with sesame seeds.
Serve the stir-fry over rice.