Begin by rinsing the long-grain rice under cold water until the water runs clear. In a large pot, combine the rinsed rice, water, vegetable broth, and salt. Bring to a boil over medium-high heat.
Once boiling, reduce the heat to low, cover the pot, and let it simmer for about 18-20 minutes, or until the rice is tender and the liquid has been absorbed. Remove from heat and let it sit covered for an additional 5 minutes. Fluff the rice with a fork and set it aside.
In a large skillet or wok, heat 2 teaspoons of vegetable oil over medium-high heat. Add the whisked eggs and cook, stirring gently, until they are scrambled and fully cooked. Transfer the scrambled eggs to a plate and set aside.
In the same skillet, add a little more vegetable oil if needed, then toss in the frozen peas and carrots. Sauté for about 2-3 minutes, until heated through and tender. Add the scallions for extra flavor.
Add the cooked rice to the skillet with the vegetables. Drizzle the sesame oil over the mixture and stir everything together, ensuring the rice is evenly distributed with the vegetables and eggs. Cook for an additional 3-5 minutes, stirring occasionally, until everything is heated through.