Bring a pot of water to a boil and cook the soba noodles according to package directions, then drain and set aside.
In a medium saucepan, combine the chicken broth, minced ginger, minced garlic, and the white parts of the sliced green onions.
Bring the broth to a gentle simmer over medium heat and stir in the tamari, white pepper, and sea salt.
Add the chopped baby bok choy to the broth and cook for 2 minutes until just tender.
In a small bowl, whisk together the whole eggs and egg whites until well combined.
Slowly drizzle the egg mixture into the simmering broth while stirring gently in a circular motion to create silky ribbons.
Place the cooked noodles into a serving bowl and pour the hot egg drop soup over the top.
Finish with a drizzle of sesame oil and garnish with the remaining sliced green onion tops.