Cook the Eggs: Bring a pot of water to a boil. Gently add the eggs and boil for 6-7 minutes for a soft-boiled consistency or 9-10 minutes for hard-boiled. Remove the eggs with a slotted spoon and immediately place them in ice-cold water to stop the cooking process. Once cooled, peel the eggs and set aside.
Prepare the Ramen and Broth: In a large pot, bring 4 cups of chicken broth to a boil. Add the ramen noodles (discard the flavor packets to reduce sodium intake) and cook according to the package instructions, about 3-4 minutes. Remove the noodles and divide them between two bowls, keeping the broth warm.
Sauté the Aromatics and Bok Choy: Heat the sesame oil in a pan over medium heat. Add the minced garlic and grated ginger, sautéing until fragrant, about 1 minute. Add the baby bok choy and sauté until the leaves wilt and the stems are tender but crisp, approximately 2-3 minutes.
Assemble the Bowls: Pour the hot broth over the noodles in each bowl. Divide the sautéed baby bok choy between the bowls. Cut the boiled eggs in half and place two halves in each bowl.
Add Toppings and Serve: Top each bowl with raw shredded carrots and sprinkle with black sesame seeds. Garnish with chopped green onions. Serve immediately, allowing each person to stir their bowl to mix the toppings with the broth and noodles.