Chicken and Walnut Fried Rice

Ingredients

• vegetable oil

  divided
  4½ teaspoons
• eggs

  beaten
  2 unit
• chopped walnuts
  ½ cup
• boneless

  skinless chicken breast, cut into strips
  ¾ pound
• ground white pepper
  ½ teaspoon
• thinly sliced fresh mushrooms
  1 cup
• thinly sliced carrots
  ½ cup
• thinly sliced green onions
  ½ cup
• grated fresh ginger
  1½ teaspoons
• cooked brown rice

  chilled
  3 cups
• soy sauce
  2 tablespoons