Bring the chicken broth to a boil in a pot, then stir in the rice. Cover, reduce the heat, and let it simmer until the rice has absorbed all the liquid (about 15 minutes). Spread it out on a tray and cool it, ideally overnight or until it's very cold, so it fries up nicely without getting mushy.
While the rice is cooling, mix up the sauce (soy sauce, beef broth, honey, hot sauce, ginger, and optional sesame oil) and toss the beef thin slices in about two tablespoons of that sauce. Tenderize the beef if needed, slice across the grain, and season it. This keeps it tender and flavorful.
Melt butter in a smaller skillet (medium-low heat) and pour in the whisked eggs. Scramble gently until just set, then remove them to set aside. This way they don’t overcook later when everything else goes in.
Heat oil in the wide skillet (medium-high), sear the beef slices (3-4 minutes per side) until browned, then take it out. Add the wine to deglaze, scraping up browned bits, and let it reduce by about half. Stir in onions, garlic, peas, and carrots.
Once those soften, add the chilled rice and the rest of the sauce, tossing constantly until the rice picks up color and absorbs most sauce. Finally fold in the beef, scrambled eggs, and green onions, warming everything together and serving hot.