In a large pot, heat the sesame oil over medium heat. Add the minced garlic and grated ginger, and sauté for about 1 minute until fragrant.
Add the chicken broth to the pot and bring it to a simmer. Season with soy sauce, salt, and pepper to taste.
While the broth is heating, place the chicken breasts in a medium saucepan and cover them with water. Bring to a boil, then reduce to a simmer. Cook for about 15 minutes, or until the chicken is cooked through. Remove from heat and let it cool slightly before shredding.
Once the broth is simmering, add the ramen noodles to the pot. Cook according to package instructions, usually around 3-4 minutes.
In the last minute of cooking the noodles, add the baby bok choy to the pot to wilt it slightly.
Divide the shredded chicken among four bowls. Once the noodles and broth are done, ladle the broth, noodles, and bok choy into each bowl.
If using, halve the soft-boiled eggs and place them on top of the ramen. Garnish with chopped green onions and a drizzle of chili oil or paste if desired.
Serve immediately and enjoy your homemade chicken ramen!