In a small bowl, beat the eggs. Heat a non-stick skillet over medium heat and add a little bit of the olive oil. Add the beaten eggs and scramble until fully cooked. Transfer to a plate and set aside.
In the same skillet, heat the remaining olive oil. Add the diced onion, minced garlic, grated ginger, and shredded carrot. Cook for about 5 minutes, or until the onion is translucent and the carrot is tender.
Add the shredded cabbage and diced bell pepper to the skillet (see note 2). Continue cooking for another 5 minutes, or until the vegetables are tender.
Add the frozen peas to the pan, then add the cooked brown rice. Stir everything together and cook for another 2-3 minutes or until the rice is heated through.
Add the cooked scrambled eggs back into the skillet. Stir to combine.
Add the low-sodium soy sauce and sesame oil to the skillet. Stir everything together until all the ingredients are well-coated. Season with salt and pepper to taste.
Garnish with the chopped green onions just before serving.