In a preheated skillet over medium-high heat, warm the sesame oil and olive oil. Add the shrimp, cook until they turn pink and opaque (about 3 minutes), flipping once. Remove them from the pan and set aside, leaving behind flavorful juices in the pan.
Into that same pan, add peas, carrots, and corn. Stir and cook for about 2 minutes until they begin to soften. Then stir in minced garlic and cook about 1 more minute until aromatic, being careful not to burn it.
Push the veggies to one side of the skillet. Pour the beaten eggs into the open side and gently scramble, stirring until just cooked through (3 to 4 minutes). Then gently mix them into the vegetables.
Return the shrimp to the skillet. Add the cooled cooked rice and sliced green onions. Drizzle soy sauce evenly over everything, season with salt and pepper, and stir thoroughly. Cook about 2 more minutes, just until everything is heated and flavors meld.