In a small bowl, whisk together soy sauce, mirin, and honey. Set aside.
Heat a swirl of olive oil in a large heavy duty skillet over medium heat until it shimmers.
Add the ground beef to the skillet and break it up into smaller pieces with a spatula. Allow to cook undisturbed for a few minutes, then flip and continue to cook until the beef is well browned on all sides. Season lightly. Drain any excess fat from the ground beef and then remove it to a plate or bowl.
Add half the butter to the wok, then add the chopped white onion and cook until it starts to become softened and translucent, about three minutes.
Add the frozen peas and carrots and continue cooking until the veggies are softened, about two minutes. Add the garlic and ginger and heat until fragrant, about 30 seconds.
Push the veggies to the side and crack the eggs into the pan. Use a spatula to scramble the egg and cook, stirring occasionally, chopping them into smaller pieces, until mostly set, a few minutes. Push the eggs to the side with the veggies, and sprinkle both with salt and pepper.
Turn the heat up to high and melt the remaining butter. Add the rice, spreading it over the pan and allowing it to cook undisturbed for a few minutes. We want to get some crispy bits!
Add the ground beef back to the pan and toss the veggies with the rice. Add the soy sauce mixture and stir until it is well combined and soaked into the rice, another few minutes.
Drizzle with sesame oil and garnish with green onion and sesame seeds, if desired.