Bring a small pot of water to a boil, carefully lower the egg into the water, and simmer for 6.5 minutes for a soft-boiled yolk. Immediately transfer to an ice bath, then peel and slice in half.
Season the chicken breast with sea salt and black pepper.
Heat the toasted sesame oil in a skillet over medium-high heat. Add the chicken and cook until golden brown and cooked through, about 5-6 minutes per side.
Remove the chicken from the skillet and let it rest before slicing into strips.
In the same skillet, add the minced garlic, grated ginger, and chopped baby bok choy. Sauté for 2-3 minutes until the greens are wilted and tender.
In a small bowl, whisk together the tahini, tamari, and 1 tablespoon of warm water until a smooth, creamy sauce forms.
Add the cooked egg noodles and sliced chicken back into the skillet with the vegetables.
Pour the sesame-ginger sauce over the noodle mixture and toss well to coat everything evenly.
Transfer the mixture to a bowl and top with the halved soft-boiled egg before serving.