Make Sauce: Whisk the sauce ingredients together; set aside.
Sauté Onion: Melt 2 tablespoons butter with 1 teaspoon oil over medium-high heat in large nonstick sauté pan. Add the chopped white onion and stir fry for 2 minutes.
Stir Fry Carrots: Add the carrots and white parts of the green onions and stir fry until onions are softened, about 5 minutes. Add the garlic and sauté 30 seconds.
Stir Fry Rice: Add an additional 1 tablespoon butter to the pan and melt. Add the rice, and stir fry one minute.
Add Peas and Sauce: Add the frozen peas and sauce; cook for 3-4 minutes, until the rice is warmed through and the sauce is absorbed (let the rice rest for a bit between stirs so that it can crisp up on the bottom).
Scramble Egg: Push the rice to the outside perimeter of the pan to make a large hole/well in the center. Add 1 teaspoon oil to the cleared space, and spread it around to cover. Pour eggs into the well, then scramble thoroughly in the cleared space (don’t "soft scramble" or the eggs will get lost).
Combine: Add the green onions, then stir everything together. Remove from heat. Season to taste with salt, pepper (I like more salt), additional soy sauce and/or chili sauce if desired.