Stir the soy sauce, brown sugar, rice vinegar, ginger, garlic, and sesame oil together in a small bowl. Set this aside.
Coat the bottom of a large nonstick skillet with half of the oil and place it over medium heat. Add the tofu cubes in an even layer (Note 2). Cook the tofu for about ten minutes, flipping the pieces about halfway through, until they are golden brown and crispy. Remove the tofu from the skillet and transfer it to a plate.
Add the remaining oil to the skillet and raise the heat to medium-high. Give the oil a minute to heat up, then add the bell pepper. Cook the pepper for about four minutes, stirring constantly, until it brightens in color and become tender-crisp.
Return the tofu to the skillet, then pour the sauce over the tofu. Stir everything up, bring the sauce to a simmer, and lower the heat slightly. Allow the sauce to simmer until most of it has dried up or been absorbed into the tofu, about three to four minutes.
Remove the skillet from heat and top the tofu with chopped scallions and sesame seeds.
Serve alone or with rice.