Meanwhile, heat olive oil in large skillet over medium-high heat. Add eggs and swirl to coat the bottom of the pan. Cook until eggs are firm and set, about 1-2 minutes. Transfer eggs to cutting board and set aside.
Add garlic and ginger to the same skillet; cook for 1 minute. Add steak and cook until cooked through; 3-5 minutes. Add the carrots, snow peas, and mushrooms. Add soy sauce and sesame oil and bring to a simmer. Stir in rice and heat through. Remove from heat and stir in scallions.
Slice eggs into thin strips. Spoon fried rice onto a serving platter, top with eggs and serve.