Place dried rice noodles in a large heatproof bowl and cover with very hot tap water, just off the boil. Soak for 8 to 12 minutes until pliable but still slightly firm, then drain and toss with 1 teaspoon oil.
Slice chicken thinly against the grain, about 1/4 inch thick. Toss with cornstarch and light soy sauce until coated, then set aside while prepping vegetables.
Mince garlic and slice chilies, keeping them together. Slice onion and bell pepper into thin strips, cut Chinese broccoli into 2-inch pieces separating stems from leaves, pick basil leaves, and beat the egg.
In a small bowl, combine oyster sauce, light soy sauce, dark soy sauce, fish sauce, sugar, chili garlic sauce, and water. Stir until sugar dissolves and sauce is evenly dark and glossy.
Heat wok over high heat for 1 minute, add 1 tablespoon oil, and sear chicken in a single layer for 1 minute without moving. Stir and cook 2 to 3 minutes until golden and cooked through, then transfer to a plate.
Return pan to high heat and add remaining 1 tablespoon oil. Stir garlic and chilies for 15 seconds until fragrant, then add onion, bell pepper, and broccoli stems and stir fry 2 minutes. Add broccoli leaves and cook 30 seconds more.
Push vegetables to one side, pour beaten egg into the empty side, and let set for 10 seconds. Scramble gently into small curds and fold into the vegetables.
Add drained noodles to the pan and pour sauce evenly over them. Gently lift and fold noodles for 2 to 3 minutes until deep golden brown, adding 1 to 2 tablespoons water if dry or sticking.
Return cooked chicken and juices to the pan and toss for 1 minute until hot and coated. Turn off heat, add Thai basil leaves, and toss for 10 seconds until wilted. Taste and adjust with fish sauce or sugar.
Divide noodles among four warm plates or bowls and serve immediately while hot and chewy.