In a small bowl, toss the sliced beef with 1 tablespoon of soy sauce. Set aside.
Heat 1/2 tablespoon of avocado oil in a large skillet or wok over medium-high heat. Add the whisked eggs, cook until softly scrambled, and transfer to a plate.
In the same skillet, add another 1/2 tablespoon of avocado oil. Add the beef and cook for 3-4 minutes until browned. Remove the beef and set it aside with the eggs.
Add the remaining 1 tablespoon of avocado oil to the skillet. Stir in the diced carrots, minced garlic, and grated ginger, cooking for 3 minutes until fragrant and slightly softened.
Add the cold cooked brown rice and frozen peas to the skillet. Toss continuously for 4-5 minutes, allowing the rice to heat through and slightly crisp.
Return the cooked beef and eggs to the skillet. Pour in the remaining 2 tablespoons of soy sauce and the sesame oil. Stir well to combine all ingredients.
Remove the skillet from the heat, stir in the sliced green onions, and serve hot.