Heat sesame oil and olive oil in a large nonstick skillet or wok over medium-high heat. Add shrimp and cook until they are bright pink on the outside and the meat is opaque, about 3 minutes, flipping halfway through.

Remove shrimp from the skillet using a slotted spoon, allowing oils and cooking juices to remain in the skillet. Place shrimp on a plate and set aside.

Add peas and carrots and corn to the skillet and cook, stirring intermittently, until vegetables begin to soften, about 2 minutes. Add garlic; cook and stir for 1 minute. Push vegetables to the side of the skillet, pour eggs into the other side, and cook to scramble, stirring as necessary, 3 to 4 minutes.

Stir shrimp, rice, and green onions into the skillet. Drizzle evenly with soy sauce, season with salt and pepper, and stir to combine. Cook until shrimp is reheated through, about 2 minutes.