In a large nonstick skillet (I use a 12-inch) or wok, heat ½ tablespoon of the vegetable oil over medium-high heat. Season the eggs lightly with salt, add them to the pan, and scramble just until cooked through. Remove the eggs from the pan to a plate and set aside.
Add an additional tablespoon of vegetable oil to the pan. Add the zucchini, mushrooms, carrots, and onions. Season lightly with salt and pepper. Stir-fry just until the vegetables begin to soften a little, about 4 to 5 minutes. Note: The vegetables will continue to cook in the next steps, so don't worry if you think they're too firm at this point.
Add the shrimp to the pan; season lightly with salt and pepper. Stir-fry just until the shrimp turns pink and is cooked through, about 4 to 5 minutes.
Add the remaining tablespoon of vegetable oil to the pan along with the garlic, green onions, soy sauce, oyster sauce, and rice. Stir-fry for another 3 to 4 minutes to fry the rice.
Turn off the heat and add the scrambled eggs and sesame oil; stir to combine. Taste and adjust seasoning/add more soy sauce if needed.
If desired, garnish with a sprinkle of sesame seeds; serve immediately.