Heat 1 tablespoon of avocado oil in a large wok or non-stick skillet over medium-high heat.
Pour in the beaten eggs and scramble until just set; immediately remove from the pan and set aside.
Add the remaining 1 tablespoon of avocado oil to the same pan. Add the diced onion and sauté for 3 minutes until translucent.
Stir in the minced garlic, grated ginger, and the frozen peas and carrots. Sauté for 2 minutes until the vegetables are tender-crisp and fragrant.
Increase the heat to high. Add the chilled brown rice to the pan, using a spatula to break up any large clumps.
Drizzle the low-sodium soy sauce and toasted sesame oil evenly over the rice. Toss continuously for 3 to 4 minutes to ensure the rice is well-coated and slightly toasted.
Add the scrambled eggs and black pepper back into the pan. Stir for 1 minute to incorporate all ingredients thoroughly.
Remove from heat, garnish with sliced green onions, and serve immediately.