Whisk eggs, milk, sugar, and seasoning salt until completely combined. Stir in green onions, Spam, and carrot.
Heat 1 teaspoon oil in a nonstick omelet pan over medium-low heat. Pour in ½ cup egg mixture, tilting the pan to evenly coat the bottom. Cook until the bottom is just set but the top is still slightly wet, 1–3 minutes.
Starting from the edge closest to you, gently fold/roll the omelet away from you a few times. Slide the partially rolled omelet back toward you to create an empty space in the pan.
Lightly oil the empty space and pour in another thin layer of egg mixture, letting it connect to the existing roll. Cook until just set but still slightly wet on top, then continue rolling the omelet away from you.
Repeat this process: oil, pour, cook, and roll until all the egg mixture is used. Cook the finished omelet, turning as needed, until sealed on all sides.
Transfer to a cutting board and rest for 5 minutes. Slice into ½-inch pieces and serve.
