Spray a large skillet with oil spray and place over medium-high heat. Once hot, add the ground beef. Crumble and cook until browned and cooked through. Drain any excess fat.
Stir in the carrot, zucchini, and spinach (or whatever vegetables you'd like to use). Lower the heat to medium and continue to cook until all the vegetables have softened, about 5 minutes.
Stir in the garlic and ginger and continue to cook for another minute.
Add the water and simmer, scraping up any brown bits stuck to the bottom of the pan.
Add the soy sauce, vinegar, sesame oil, honey, and gochujang. Stir well to combine. Taste and add more seasonings as desired. Keep warm over low heat.
Before serving, fry the eggs in a separate non-stick skillet to your preference.
Serve the ground beef mixture and eggs, if using, over rice. Top with scallions and sesame seeds.