Heat 1 tablespoon of vegetable oil in a large skillet over medium heat. Crack the eggs into the pan and scramble them until just set. Remove the eggs to a plate and set aside.
Add the remaining tablespoon of vegetable oil to the same skillet. Stir in the garlic and cook for 30 seconds until fragrant.
Add the frozen mixed vegetables and diced bell pepper. Cook for 3 to 4 minutes, stirring often, until the vegetables are warmed through.
Add the day-old rice and break up any clumps. Pour in 3 tablespoons of soy sauce and the sesame oil. Stir-fry everything together for 3 minutes.
Return the scrambled eggs to the skillet along with most of the sliced green onions. Toss to combine and heat through for 1 minute.
Divide the fried rice among bowls. Drizzle the remaining tablespoon of soy sauce over each serving and finish with the rest of the green onions.