Bring a small pot of water to a boil and carefully lower the egg into the water; simmer for 7 minutes, then transfer to an ice bath, peel, and set aside.
In a medium saucepan, combine the water, minced garlic, and grated ginger, bringing the mixture to a gentle simmer over medium heat.
Slice the chicken breast into thin strips and add them to the simmering broth along with sea salt and black pepper, cooking for about 5 minutes until fully opaque.
Add the dry soba noodles to the pot and cook according to package directions, usually about 4 to 5 minutes, until tender.
Turn off the heat and whisk in the white miso paste and tamari until fully dissolved, ensuring the broth does not boil again to preserve the miso's nutrients.
Stir in the baby spinach until just wilted, then ladle the soup and noodles into a large bowl.
Slice the soft-boiled egg in half and place it on top of the noodles, finishing the dish with a garnish of crisp sliced scallions.