Bring water and quinoa to a boil in a saucepan; season with salt. Reduce heat to medium-low, cover, and simmer until quinoa is tender and water has been absorbed, 15 to 20 minutes. Remove saucepan from heat and let sit for 5 minutes; fluff quinoa with a fork. Refrigerate until cool, 8 hours to overnight.

Mix soy sauce, teriyaki sauce, and sesame oil together in a bowl until sauce is evenly mixed.

Heat 1 1/2 teaspoons oil in a large skillet over high heat; saute carrots and onion for 2 minutes. Add 2 scallions, garlic, and ginger; saute until fragrant, about 2 minutes more. Add the remaining 1 1/2 teaspoons oil and quinoa; cook until heated through, about 2 minutes.

Stir sauce into quinoa mixture; cook and stir until evenly coated, about 2 minutes.

Make well in the center of the quinoa mixture. Pour eggs into the well; cook and stir until eggs are scrambled and cooked through, 2 to 3 minutes. Add peas and cook until heated through, 2 to 3 minutes. Add remaining scallion.