Cook the soba noodles in boiling water according to package instructions, then drain and set aside.
Slice the chicken breast into thin, bite-sized strips.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Add the chicken strips to the skillet and sauté until golden brown and fully cooked through.
Add the minced garlic, grated ginger, julienned carrots, and sliced red bell pepper to the pan, stir-frying for 3 minutes.
Stir in the chopped bok choy and cook for 1-2 minutes until the leaves are just wilted.
In a small bowl, whisk together the tamari, rice vinegar, and red pepper flakes.
Add the cooked soba noodles and the sauce mixture to the skillet, tossing everything together until the noodles are well coated and heated through.
Serve immediately topped with freshly sliced green onions.