Step 1: Prepare the marinade. In a medium bowl, whisk together 1/4 cup soy sauce, rice vinegar, 1 tablespoon sesame oil, cornstarch, 1 teaspoon grated fresh ginger, 2 cloves minced garlic, and brown sugar.
Step 2: Add the cut chicken to the marinade, ensuring all pieces are well coated. Cover and refrigerate for at least 30 minutes, or up to 4 hours for best flavor.
Step 3: While the chicken marinates, prepare your vegetables. Slice the bell peppers and onion. Separate broccoli into florets. Mince the additional 2 cloves of garlic and grate the additional 1 teaspoon of fresh ginger.
Step 4: Preheat your Blackstone griddle to medium-high heat. Add 1-2 tablespoons of high-smoke point oil to the griddle. Once shimmering, spread the marinated chicken in a single layer. Cook for 5-7 minutes, flipping occasionally, until the chicken is golden brown and cooked through. Remove the chicken from the griddle and set aside.
Step 5: Add another tablespoon of oil to the griddle. Add the sliced bell peppers, onion, and broccoli florets. Stir-fry for 5-7 minutes, until the vegetables are tender-crisp.
Step 6: Push the vegetables to one side of the griddle. Add the minced garlic and grated ginger to the empty space and cook for about 30 seconds until fragrant, being careful not to burn.
Step 7: Return the cooked chicken to the griddle with the vegetables. Pour the remaining 1/4 cup of soy sauce and oyster sauce (if using) over the mixture. Toss everything together to combine and allow the sauce to thicken slightly, cooking for another 2-3 minutes.
Step 8: Garnish with chopped green onions and sesame seeds. Serve immediately over cooked white rice or noodles.