Heat the 1/2 tablespoon olive oil in a skillet over low heat. Add the diced shallot and onions and cook for 10 to 12 minutes, stirring occasionally, until tender. Set aside.
Heat the olive oil over low heat in a large skillet. Add the onion mixture then stir in the brown rice, soy sauce, and vinegar, and cook for 2 to 3 more minutes. Create a well in the center and crack the eggs. Let them set most of the way, 3 to 4 minutes, before stirring them into the rice mixture. Stir in the sesame seeds and black pepper. Serve hot.