Begin by cooking the brown rice according to the package instructions, usually involving rinsing and simmering for 40-45 minutes.
In a large skillet or wok, heat 1/2 tablespoon of olive oil over medium-high heat. Add chicken and cook for 5-7 minutes until browned. Remove and set aside.
Add the remaining olive oil, onion, and sauté for 2 minutes. Then add garlic and carrots, cooking for another minute.
Stir in the cabbage and cook for 3-4 minutes. Add chili pepper if using.
Return the chicken to the skillet with rice, soy sauce, and sesame oil. Cook for 2-3 minutes until heated through.
Fold in mung bean sprouts and toss gently before serving.
Serve hot, garnished with extra bean sprouts or green onions if desired.