Bring a pot of water to a boil and cook the soba noodles for approximately 4-5 minutes until tender, then drain and rinse with cold water to stop the cooking process.
Slice the chicken breast into thin, bite-sized strips and chop the bok choy into 1-inch pieces, keeping the white stems and green leaves separated.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken strips to the skillet and cook for 5-6 minutes, stirring occasionally, until golden brown and cooked through.
Stir in the minced garlic, grated ginger, and red pepper flakes, sautéing for about 1 minute until the fragrance is released.
Add the bok choy stems to the pan and cook for 2 minutes, then toss in the green leaves and cook for another minute until they are just wilted.
Pour in the tamari and rice vinegar, tossing all ingredients together to coat them evenly in the sauce.
Divide the cooked soba noodles into bowls, top with the chicken and bok choy stir-fry, and garnish with sesame seeds.