Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the diced chicken breast to the pan, seasoning with sea salt and black pepper; cook until golden and cooked through, about 5-6 minutes.
Add the shrimp to the pan and sauté until pink and opaque, approximately 2-3 minutes; remove both the chicken and shrimp from the pan and set aside.
In the same pan, add the minced garlic, grated ginger, and frozen peas and carrots, stir-frying for 2-3 minutes until fragrant and tender.
Add the chilled brown rice to the pan, breaking up any clumps with a spatula, and cook for 2 minutes until the grains are slightly toasted.
Return the cooked chicken and shrimp to the pan, then drizzle with the tamari and toasted sesame oil.
Toss all ingredients together for 1-2 minutes until well combined and thoroughly heated through.
Remove from heat and garnish with sliced green onions before serving.