Step 1: In a medium bowl, combine the chicken pieces with 1 tablespoon of soy sauce, 1 teaspoon of sesame oil, and black pepper. Toss to coat and let marinate for at least 10 minutes while you prepare the vegetables.
Step 2: In a small bowl, whisk together the gochujang, remaining 1 tablespoon of soy sauce, rice vinegar, brown sugar, remaining 1 teaspoon of sesame oil, cornstarch, and water/chicken broth until smooth. Set aside.
Step 3: Heat 1 tablespoon of neutral cooking oil in a large wok or heavy-bottomed skillet over high heat until shimmering and lightly smoking.
Step 4: Add the marinated chicken to the hot pan, spreading it into a single layer. Cook for 3-4 minutes, undisturbed, until browned on one side. Flip and cook for another 2-3 minutes until almost cooked through. Remove the chicken from the pan and set aside.
Step 5: Add the minced garlic and grated ginger to the same pan. Stir-fry for about 30 seconds until fragrant, being careful not to burn them.
Step 6: Add the broccoli florets and sliced carrots (if using) to the pan. Stir-fry for 2-3 minutes until they begin to tenderize but are still crisp-tender.
Step 7: Add the sliced red and yellow bell peppers and sliced onion to the pan. Stir-fry for another 2-3 minutes until the vegetables are tender-crisp.
Step 8: Return the cooked chicken to the pan. Give the prepared gochujang sauce a quick whisk to recombine any settled cornstarch, then pour it over the chicken and vegetables.
Step 9: Stir continuously for 1-2 minutes, allowing the sauce to thicken and coat all the ingredients evenly. The sauce should become glossy.
Step 10: Remove from heat immediately. Taste and adjust seasoning if desired (e.g., more soy sauce for saltiness, more brown sugar for sweetness, or a pinch of red pepper flakes for extra heat).
Step 11: Serve hot over cooked rice, garnished with toasted sesame seeds and sliced green onions, if using. Enjoy your delicious Gochujang Stir Fry!