Place eggs in a small pot of boiling water and cook for 6 minutes and 30 seconds. Immediately transfer to an ice bath, peel when cooled, and set aside.
In a large pot, heat sesame oil over medium heat. Add minced garlic and grated ginger, sautéing for 1-2 minutes until fragrant.
Add the thinly sliced chicken breast to the pot and sear until browned on both sides and cooked through (approximately 5-6 minutes).
Pour in the chicken bone broth and soy sauce. Bring the liquid to a gentle simmer.
Add the ramen noodles to the simmering broth. Cook according to package instructions, typically 3 to 4 minutes.
Stir in the baby spinach during the final 60 seconds of noodle cooking until just wilted.
Divide the noodles, chicken, and broth evenly into two large bowls.
Slice the soft-boiled eggs in half and place them on top of each bowl.
Garnish with sliced green onions and chili flakes before serving.