Heat a large skillet over medium-low heat and add 2 tablespoons sesame oil.
Add 2/3 cup diced sweet onions, 1 cup diced (thawed) carrots, and 1 cup (thawed) peas to the skillet. Sauté, stirring occasionally, until the vegetables are tender, about 8–10 minutes.
While the vegetables cook, crack 2 large eggs into a small bowl and whisk with a fork until combined; set aside.
Increase the heat to medium. Add 2 cups cooked, shredded chicken and 4 cups cooked, chilled brown rice to the skillet with the vegetables. Stir and break up any clumps, cooking until the chicken and rice are heated through, about 3–5 minutes.
Push the rice and vegetable mixture to one side of the skillet to clear a space. Pour the whisked eggs into the cleared space and scramble them until just set, about 1–2 minutes.
Stir the scrambled eggs into the rice mixture. Add 3 to 4 tablespoons lite soy sauce (or gluten-free tamari) and stir thoroughly to coat and evenly season the rice. Cook 1 more minute to combine flavors, then remove from heat and serve.