Whisk together ¾ cup rice vinegar, ½ cup water, 1 tablespoon honey, and ¾ teaspoon salt until dissolved. Add sliced cucumbers and set aside.
Heat 1 tablespoon oil in large sauté pan over medium-high heat. Add shredded carrots with ½ teaspoon salt and cook 10-15 minutes until softened and starting to char. Transfer to bowl.
Heat 2 teaspoons oil in pan over medium heat. Add grated onion, garlic, ginger, and ½ teaspoon black pepper. Cook 3 minutes until starting to brown.
Add ground beef and break into small pieces. Cook until no longer pink, about 5-7 minutes. Drain excess fat.
Return beef to pan and stir in honey, soy sauce, gochujang, and mirin. Cook 3 minutes until sauce thickens.
Season to taste with additional soy sauce and honey. Serve in lettuce cups with pickled cucumbers, carrots, and rice.
Notes
Use 90% lean ground beef for best flavor and texture balance.
Grate onion using box grater for better flavor distribution.
Fresh garlic and ginger are essential for authentic flavor.
For gluten-free: use tamari and gluten-free gochujang.