Preheat the oven to 425°F (220°C).
In a large bowl, toss the shrimp with 1 tablespoon of vegetable oil, 1/4 teaspoon salt, and 1/4 teaspoon black pepper. Spread the shrimp evenly on one side of a large rimmed sheet pan.
In the same bowl, combine the chilled cooked rice, thawed peas and carrots, diced onion, minced garlic, grated ginger, and beaten eggs. Drizzle with 1 tablespoon vegetable oil and 1 tablespoon soy sauce. Mix well to evenly coat the rice and vegetables.
Spread the rice mixture evenly on the other side of the sheet pan, keeping it separate from the shrimp.
Place the sheet pan in the oven and bake for 12 minutes.
Remove the sheet pan from the oven and stir the rice mixture to break up any clumps. Flip the shrimp over to cook the other side.
Drizzle the rice with the remaining 1 tablespoon soy sauce and sesame oil. Return the sheet pan to the oven and bake for an additional 8 minutes, or until the shrimp are pink and opaque and the eggs in the rice are fully cooked.
Remove from the oven and sprinkle sliced green onions over the entire sheet pan.
Gently toss the shrimp and fried rice together on the sheet pan to combine all ingredients before serving.