In bowl, combine soy sauce, brown sugar, sesame oil and garlic. Add beef and mix well. Refrigerate marinated beef at least 30 minutes, or overnight.
Prepare rice according to package directions.
Heat skillet over medium-high heat. Cook beef 7 minutes, stirring often, until cooked through and caramelized. In last 3 minutes, add carrots, cucumbers and onions.
Divide rice between bowls. Top with beef bulgogi. Garnish with green onions and sesame seeds.