Fill a large pot with enough water to cover the eggs. Bring to a boil, and then use a large spoon to lower the eggs into the boiling water. Simmer for 6-8 minutes (6 minutes for a slightly runny yolk; up to 8 minutes for a firmer, but still soft yoke). While it's simmering, you can start on the ramen. Once done, remove from water and gently place immediately into an ice bath (large bowl filled with ice and cold water), then peel and slice in half.
Make the ramen broth & noodles
In a large pot or saucepan, heat the sesame oil and olive oil together over medium-high heat. Add garlic and ginger and sauté for just 1 minute.
Add the chicken and carrots, sauté for one more minute.
Slowly add the broth and bring to a boil.
Add the ramen noodles, soy sauce or coconut aminos, and oyster sauce, and cook over medium heat for about 2-3 minutes, until the noodles are cooked through to your liking.
Remove from heat and season with salt and pepper to taste. Top with green onions, sesame seeds. Enjoy immediately.
Notes
CHICKEN: To save time, use chicken breast shredded from a cooked deli rotisserie chicken. SOY SAUCE/COCONUT AMINOS: Start with 2 tablespoons then if you find you want a bit more flavor, add another tablespoon. I use coconut aminos in place of soy sauce because it's gluten-free and I like the flavor, but you can use any soy sauce as well.OYSTER SAUCE: If you don't have oyster sauce, you can either eliminate it all together, or simply add an extra teaspoon or two of soy sauce or coconut aminos.