As the meat needs to be marinated for an hour, start with that. I use a plastic bag as it is easy and saves time, but if you want to use a bowl that's fine too. Combine the beef, scallion, onion, carrot, soy sauce, honey sesame oil, sesame seeds, rice wine and red pepper flakes (optional) and mix well. Seal and place in the fridge for an hour.
When there is about 10 minutes left to marinate the meat, take a saucepan on medium-low heat and crush the anchovy fillet with two forks until you make a paste. Whisk it with the water. It is okay if it is not homogeneous at this point. Turn the heat up high and reduce the water about 75%. Begin making the rice.
Remove the bulgogi from the fridge and pour the whole bag into your simmering pan. If your saucepan is small you can do it in multiple batches. Let cook, stirring often for about 1-2 minutes. You can remove the meat early and let the veggies cook for longer if you want them to be softer.
Divide into 4 portions and serve over 4 bowls of rice, liquid and all.