Preheat the oven to 425F and line a sheet pan with parchment paper.
Spread the rice in an even layer and top with the onion, carrot, scallions, salt, pepper, soy sauce, sesame seeds, and sesame oil. Drizzle some of the sesame oil around the edges of the rice for extra crispiness.
In a small bowl, combine the garlic and butter. Microwave until melted or melt in a pan, stir, and drizzle evenly over the rice.
Use two spoons to make two small wells in the rice, then crack an egg into each one.
Bake for 15 minutes, until the rice is crisp at the edges and the eggs are cooked through. Slice the eggs into small pieces with two knives, then toss until evenly combined.
