In large bowl, combine soy sauce and sesame oil. Add chicken and stir to combine. Set aside.
While chicken is marinating, heat a 10 or 12 inch skillet over medium heat. Add 1 teaspoon vegetable oil to pan. Add eggs; swirl and flip to form omelet. Remove omelet from pan, roll into tube and slice into thin slices. Reserve.
Heat large sauté pan or wok over medium heat. Add 1 tablespoon vegetable oil. Add chicken and toss until cooked through, about 5 minutes. Add 1 tablespoon vegetable oil to pan and heat. Add mushrooms and sauté, stirring until browned. Add asparagus pieces, tossing until just tender, another 4 – 5 minutes. Add scallions and sauté 2 minutes.
Add vinegar and oyster sauce to vegetables. Add rice and toss, heating thoroughly, about 4 minutes. Add peas and return chicken to pan. Add reserved egg, warm through and serve immediately.