Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add diced onion and garlic; sauté until fragrant and translucent, about 2 minutes.
Stir in carrots, peas, and red bell pepper; cook until tender, about 4-5 minutes.
Push vegetables to one side of the pan and pour in the beaten eggs on the empty side.
Scramble the eggs until cooked through, then mix with the vegetables.
Add the remaining oil and then the chilled rice, breaking up any clumps with a spatula.
Pour soy sauce, oyster sauce (if using), and sesame oil over the rice; stir well to combine.
Cook all together, stirring frequently, for another 5 minutes until rice is heated through.
Season with salt and pepper to taste, then remove from heat and garnish with sliced green onions.