Ginger Fried Rice

In a large 12-inch nonstick skillet, heat 1 tsp. oil over medium heat. Pour in eggs and cook, stirring until softly scrambled, about 1 minute. Remove eggs to a plate. Heat 2 tsp. oil in skillet. Add shiitakes and 1/4 tsp. salt. Cook, stirring frequently, until mushrooms are tender and lightly browned, about 4 minutes. Add to eggs. Add 2 Tbsp. oil to skillet; increase heat to medium-high. Add ham, scallions, ginger, and garlic. Cook, stirring constantly for 2 minutes. Stir in rice, peas and carrots, and remaining salt. Cook, stirring frequently, until rice is hot, about 3 minutes. Stir in eggs, mushrooms, soy sauce, and sesame oil. Cook, stirring, 1 to 2 minutes.