Bring the barley and water up to a boil, cover, and reduce to a simmer. Cook the barley according to your package instructions. This might take anywhere from 45 mins to an hour. It also depends on how chewy you want it to be. Let stand covered for 5 minutes off the heat and fluff with a fork. Toss with a little sesame oil if desired.
Mix all the ingredients for the Gochujang Vinaigrette together in a bowl. Set aside.
In a pan, heat ½ a tablespoon of sesame oil over medium-high heat. Add the beef and break it up with a wooden spoon. Season lightly with salt. Cook the beef until there’s no more pink. Mix the soy sauce, sugar, sesame oil, and garlic together in a small bowl and add it to your beef. Stir well to make sure all the beef is covered with the sauce.
Assemble your individual bowls with lettuce, barley, beef, carrots, and cucumber. Top with the fried eggs and drizzle with the Gochujang Vinaigrette to taste. Sprinkle with sesame seeds if desired. Grab a fork and nom nom nom!