Begin by melting the butter in a large skillet or wok over medium heat. Add the diced onion and sauté for about 3-4 minutes until it becomes translucent. Then, stir in the minced garlic and cook for an additional 30 seconds until fragrant.
Now, toss in the frozen mixed vegetables. Stir them into the onion and garlic mixture, cooking until they're heated through, which should take about 5 minutes.
Next, add the prepared white rice to the pan. Break up any clumps with your spatula and stir everything together to combine thoroughly.
Pour in the sesame oil and soy sauce. Sprinkle the ground black pepper over the mixture and stir again, allowing the rice to cook for an additional 5 minutes, stirring occasionally.
In a small bowl, beat the eggs lightly. Push the rice mixture to one side of the skillet, creating space to scramble the eggs. Pour the beaten eggs into the empty side and scramble them until fully cooked. Mix the scrambled eggs into the rice.
Taste the fried rice and adjust the seasoning if necessary. Serve when everything is well combined and heated through!