Rinse jasmine rice thoroughly under cold running water. Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and water has been absorbed, 20 to 25 minutes, or cook according to package directions.
Spread cooked rice evenly over a large baking sheet; cool to room temperature, about 15 minutes. Chill rice, uncovered, until cold, about 30 minutes. Stir together butter and garlic in a small bowl.
Preheat an outdoor griddle to high heat (400 degrees F to 450 degrees F/200 degrees C to 220 degrees C). Add vegetable oil to griddle and heat until shimmering. Whisk together eggs, sesame oil, salt, and pepper in a small bowl. Cook eggs in hot oil, gently folding with a spatula, until eggs reach desired consistency, about 30 seconds.
Add chilled rice, and cook, turning with spatula, until rice grains are separated and coated in oil and starting to pop, about 3 minutes. Add peas and carrots and green onions; cook, turning with spatula, until softened and heated through, about 2 minutes. Add soy sauce, mirin, and butter mixture; cook and turn until evenly coated, about 1 minute. Serve with desired serve-alongs. Recipe developed by Craig Ruff