In a small bowl, whisk together soy sauce, brown sugar or honey, sesame oil, garlic, ginger, rice vinegar, and gochujang.
Heat olive oil in a large skillet over medium-high heat.
Season chicken lightly with salt and pepper.
Cook chicken for 5–6 minutes per side until golden brown and fully cooked.
Pour Korean BBQ sauce into skillet and cook for 2–3 minutes until sauce thickens and coats chicken.
Remove chicken from skillet and slice into bite-sized pieces. Toss chicken back into sauce.
Divide cooked rice among serving bowls.
Top with chicken, cucumber, carrots, avocado, and edamame.
Garnish with sesame seeds and green onions.
Serve warm with optional toppings if desired.