Heat 1 tablespoon of butter in a large sauté pan over medium-high heat until melted.
Add carrots, onion, and saute for 5-6 minutes until lightly browned and beginning to soften. Add in the peas, corn and garlic, and season with a generous pinch of kosher salt and freshly cracked pepper. Saute for about 3-4 minutes or until the veggies are heated through. Increase heat to high, add in the remaining tablespoons of butter, and stir until melted. Immediately add the rice, green onions, soy sauce and stir until combined. Continue stirring for an additional 3 minutes to fry the rice. Then spread the rice into a thin layer and let cook for 2-3 minutes until it is lightly seared on the bottom.
Then push all of the rice to one side of the pan and add in the eggs and stir to scramble. Cook the egg about 3/4 of the way done and then begin to incorporate into the rice. This will make for a smaller egg bite and incorporate it into the rice better. Remove from heat, and stir in the sesame oil until combined. Taste and season with extra soy sauce, if needed.
Serve immediately, or refrigerate in a sealed container for up to 3 days