Break the eggs into a small bowl. Beat them with a fork or small whisk.
Heat 1½ tablespoons of the butter and all of the sesame oil in a large wok or skillet over medium heat.
Slowly and carefully (to avoid being splattered by hot oil!) add the scallions, chopped vegetables, ginger, and garlic. Sauté the vegetables for a minute, stirring constantly.
Add the rice and heat for 2 to 3 minutes, stirring occasionally.
Push the rice to the edges of the pan, and add the remaining ½ tablespoon butter into the center. Add the eggs and stir until they are cooked and scrambled.
Stir the eggs into the rice until everything is mixed up. Add the soy sauce and heat for another minute or two, stirring often. Serve with additional soy sauce.
