Rinse shrimp and pat dry. Place in a bowl and season with ¼ teaspoon each of salt and pepper. Stir to mix well.
In a small bowl, mix together the soy sauce, sesame oil, and brown sugar. Set them aside.
In a large pan over medium high heat, drizzle 2 tablespoons of oil. When hot, add the shrimp in one layer and cook for about 1 minute, flipping once. Shrimp should be pink and no longer transparent. Remove from the pan and set aside.
In the same pan, add 1 tablespoon of oil, along with the chopped onions, white parts of the green onions, garlic, and ginger. Sauté for 1-2 minutes or until fragrant.
Stir in the peas and carrots and cook for about 2 minutes.
Scoot the vegetables over to one side of the pan and add 1 tablespoon of butter to the empty side. Pour in the scrambled eggs and cook until set, breaking eggs into small pieces with a spatula.
Add the shrimp, rice, and soy sauce mixture and stir well to combine. Garnish with chopped green onions and season with salt and pepper to taste. You can also drizzle extra soy sauce as desired.