Heat the vegetable oil in a large wok or pan. Add the sweet yellow onion, white portion of the green onion, and carrots then cook, stirring occasionally, for 3-4 minutes, or until tender. Add the shiitake mushrooms to the pan and cook, stirring occasionally, for 2-3 minutes. Add the garlic and ginger to the pan. Sauté for 60 seconds then add the soy sauce and white pepper along with the rice, peas, most of the green part of the green onions, and peas. Mix the rice thoroughly.