Bring a large pot of water to boil for the ramen noodles. While water heats, prepare the sauce by mixing soy sauce, oyster sauce, sesame oil, sugar, and white pepper in a small bowl. Set aside.
Heat 1 tablespoon vegetable oil in a large wok or skillet over high heat. Once shimmering, add chicken pieces and stir-fry until golden brown and cooked through, about 5-6 minutes. Remove chicken from pan and set aside.
Add remaining tablespoon of oil to the same pan. Stir-fry bell pepper, snap peas, and carrot for 2-3 minutes until crisp-tender.
Add minced garlic, ginger, and white parts of green onions to the vegetables. Stir-fry for 30 seconds until fragrant.
Meanwhile, cook ramen noodles in boiling water for 2 minutes only (slightly undercooked). Drain well and shake off excess water.
Return cooked chicken to the pan with vegetables. Add drained ramen noodles and pour sauce over everything. Using tongs, toss everything together for 2-3 minutes until well combined and heated through.
Garnish with green parts of sliced green onions. Serve immediately while hot.