Stir together the shrimp, garlic, ginger, sliced green onions, and one tablespoon of olive oil in a small bowl.
Heat the other tablespoon of the olive oil in a large skillet or wok over medium-high heat. When the oil is hot then add in the shrimp and cook until pink and opaque. This step should take about 3-4 minutes.
Remove the shrimp from the pan and place it into a clean bowl. Drain any liquid from the bowl and then stir in the teriyaki sauce.
In the same pan, add the beaten eggs and cook until just set. This step takes about 1-2 minutes. Place the eggs on top of the shrimp into the bowl.
Add the frozen vegetables to the same pan and cook on medium-high heat until vegetables are heated through, about 4- 5 minutes. Drain any excess water from the pan.
Heat one tablespoon of sesame oil in the pan and then place the rice in. Let the rice cook in the pan for about 2 minutes and then stir and cook for another 2 minutes. This step helps to create crispy pieces of rice.
Stir in the shrimp, eggs, soy sauce, sesame oil, chili oil, and vegetables, and cook for another 2 minutes or until heated. Serve hot.