1. Place eggs in a large saucepan and cover with cold water by 1 inch. Bring to a boil and cook for 1 minute. Cover eggs with a tight-fitting lid and remove from heat; set aside for 8-10 minutes. Drain well and let cool before peeling and halving. 2. Heat olive oil in a large stockpot or Dutch oven over medium heat. Add garlic and ginger, and cook, stirring frequently, until fragrant, about 1-2 minutes. 3. Whisk in chicken broth, mushrooms, soy sauce and 3 cups water. 4. Bring to a boil; reduce heat and simmer until mushrooms have softened, about 10 minutes. Stir in Yaki-Soba until loosened and cooked through, about 2-3 minutes. 5. Stir in spinach, Narutomaki, carrot and green onions until the spinach begins to wilt, about 2 minutes. 6. Serve immediately, garnished with eggs.