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Preheat oven to 375°F (190°C).
In a large saucepan, heat vegetable oil and sesame oil.
Add ginger and garlic, cook another minute, then add chicken breasts. Season generously with salt and pepper.
Sear over medium-high heat for 3 to 4 minutes on each side. Transfer chicken to a baking sheet and roast in oven for 15 minutes. Once chicken is cooked through and nicely browned, slice finely.
In the same saucepan, over medium heat, add soy sauce and fish sauce. Mix well.
Add chicken broth, chili flakes, star anise, dried mushrooms, carrots, and sweet potatoes. Bring to a boil, lower heat, and simmer 10 minutes. Taste broth and correct seasoning if desired.
Cook eggs in boiling water* for 7 minutes and transfer directly to a large bowl of ice water to stop them from cooking. The yolk should be soft-cooked and brightly colored. Peel carefully and set aside.
Divide noodles between 2 large bowls. Pour broth and vegetables over noodles and add slices of roasted chicken. Add a little fresh spinach, kale, or broccoli rubble directly to the broth (it’ll cook in the heat) then top with halved eggs and green onions.
*Reserve egg cooking water to cook ramen noodles according to the package instructions.