Drain liquid out of tofu. You can do this by placing tofu block on a large plate and covering with a cutting board or another plate. Then put something heavy (like a full teapot) on top and let drain for at least 30 minutes.
Discard the liquid and cut tofu into ½ inch cubes. Sprinkle cornstarch on tofu and lightly cover on all sides.
In a medium pot, heat 1 tablespoon sesame oil over medium heat. Add rice and stir to coat. Add water, bring to a boil, cover and reduce heat and cook until fluffy.
Meanwhile, in a medium sized bowl, combine ginger, garlic, soy sauce, water, and brown sugar. Mix until all sugar is dissolved. Set aside.
Heat remaining 1 tablespoon sesame oil in a non-stick pan over medium-high heat. Add tofu and cook until browned (about 5 minutes), then flip and brown on opposite side (an additional 5 minutes).
Add soy sauce mixture to pan, bring to a boil, and reduce heat. Stir to make sure tofu is covered. Once liquid starts to thicken, add in green beans and cook for 3-4 minutes.
Serve tofu and green beans over rice. Top with scallions and sesame seeds.