Bring a pot of water to a boil and cook the soba noodles according to package directions, then drain and set aside.
In a small bowl, whisk together the gochujang, tamari, and honey until smooth to create the stir-fry sauce.
Dice the chicken breast into bite-sized pieces and season with sea salt and black pepper.
Heat the sesame oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and cook for 5-6 minutes until golden brown and cooked through.
Stir in the minced garlic and grated ginger, cooking for 30 seconds until fragrant.
Add the broccoli florets and sliced red bell pepper to the pan, sautéing for 3-4 minutes until the vegetables are tender-crisp.
Add the cooked soba noodles and the gochujang sauce to the skillet, tossing everything together for 1-2 minutes until the sauce is thickened and well-distributed.
Serve immediately while hot.