In a small bowl, whisk together the gochujang, tamari, rice vinegar, and grated fresh ginger to create the stir-fry sauce.
Cut the chicken breast into bite-sized cubes and season evenly with sea salt and black pepper.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and cook, stirring occasionally, until golden brown and cooked through, approximately 5-6 minutes.
Remove the chicken from the pan and set aside; add the broccoli florets and sliced red bell pepper to the same pan.
Add a tablespoon of water to the vegetables and cover for 2 minutes to steam-fry until they are tender-crisp.
Stir in the minced garlic and cook for 30 seconds until fragrant, then return the chicken to the pan.
Pour the gochujang sauce over the chicken and vegetables, tossing constantly for 1 minute until the sauce thickens and coats everything beautifully.
Serve the spicy stir-fry over the warm, cooked brown rice.