Stir together oyster sauce, fish sauce, soy sauce, and brown sugar in a small bowl. Set aside.

Heat 1/2 tablespoon oil in a large cast iron skillet or wok over medium heat. Add shrimp, 1/4 cup green onions, and 1 tablespoon garlic. Cook, stirring constantly, until shrimp are firm and opaque, 3 to 4 minutes. Transfer to a bowl.

Without cleaning the skillet, add another 1/2 tablespoon oil over medium heat. Add remaining 1/4 cup green onions, remaining 1 tablespoon garlic, and mixed vegetables. Cook, stirring often, until vegetables are tender, about 4 minutes.

Push vegetables to the side of the skillet and add another 1 tablespoon oil to the center. Add beaten egg and let sit for 20 seconds; then stir gently until large curds form, about 1 minute. Stir cooked eggs and vegetables together.

Increase heat to medium-high and add remaining 1 tablespoon oil. Stir in cooked rice and reserved sauce; flatten rice in skillet. Cook, flipping and turning occasionally, until rice is brown and crispy in some spots, about 5 minutes.