Chicken Fried Rice

1 package (12 ounces) frozen mixed vegetables
2 tablespoons olive oil, divided
2 large eggs, lightly beaten
4 tablespoons sesame oil, divided
3 packages (8.8 ounces each) ready-to-serve garden vegetable rice
1 rotisserie chicken, skin removed, shredded
1/4 teaspoon salt
1/4 teaspoon pepper

Prepare frozen vegetables according to package directions. Meanwhile, in a large skillet, heat 1 tablespoon olive oil over medium-high heat. Pour in eggs; cook and stir until eggs are thickened and no liquid egg remains. Remove from pan.
In same skillet, heat 2 tablespoons sesame oil and remaining 1 tablespoon olive oil over medium-high heat. Add rice; cook and stir until rice begins to brown, 10-12 minutes.
Stir in chicken, salt and pepper. Add eggs and vegetables; heat through, breaking eggs into small pieces and stirring to combine. Drizzle with remaining 2 tablespoons sesame oil.