For the beef: Add the beef to a medium skillet over medium-low heat. Cook, breaking up with a wooden spoon and slowly rendering the fat, 8 to 10 minutes. Using a large spoon remove half of the rendered fat and discard. Add the garlic, scallions and ginger and cook an additional 2 to 3 minutes. Set aside.
For the sauce: Stir together the soy sauce, gochujang, honey and sesame oil in a small bowl. Stir some of the sauce into the beef, a few tablespoons at a time, until seasoned to your taste. Set aside.
For the sticky rice: Rinse the rice until the water runs clear. Combine the rice, oil and 1 1/2 cups water in a pressure cooker or Instant Pot®. Cook on high pressure, 8 minutes. Allow the steam to release slowly, for about 5 minutes, then remove the lid. Roll the beef, sticky rice, sauce and cucumber slices in lettuce leaves and eat.