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 paste, tamari, rice vinegar, and red pepper flakes until smooth.
Heat the sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken breast pieces to the skillet and cook until browned and fully cooked through, approximately 5 to 7 minutes.
Stir in the minced garlic and fresh ginger, sautéing for about 30 seconds until the aroma is released.
Add the broccoli florets, sliced red bell pepper, and snap peas to the pan, stir-frying for 3 to 4 minutes until they are tender-crisp.
Pour the prepared gochujang sauce over the chicken and vegetables, tossing constantly to coat everything evenly.
Divide the cooked soba noodles into bowls, top with the spicy chicken stir-fry, and garnish with sesame seeds before serving.