If making pickled cucumbers, whisk together 3/4 cup rice vinegar, 1/2 cup water, 1 tablespoon honey, and 3/4 teaspoon salt until dissolved. Add thinly sliced cucumbers and set aside for at least 15 minutes.

Heat 2 teaspoons olive oil in a large sauté pan over medium heat. Add grated onion, minced garlic, grated ginger, and 1/2 teaspoon black pepper. Cook for 3 minutes, stirring occasionally, until mixture turns golden brown and becomes fragrant.

Add ground beef to the pan and cook, breaking it into small crumbles with a wooden spoon, until no longer pink and reaches 160°F (about 6-8 minutes). Drain any excess fat and return beef to pan.

Stir in honey, soy sauce, gochujang, and mirin. Cook for 3 minutes until sauce reduces and coats the meat with a glossy sheen. Taste and adjust seasoning with additional honey or soy sauce as needed.

If making carrots, heat 1 tablespoon oil in a separate pan over medium-high heat while the beef cooks. Add shredded carrots with 1/2 teaspoon salt and cook 10-15 minutes, stirring occasionally, until softened and slightly charred.

Serve bulgogi in bibb lettuce cups or over rice with pickled cucumbers, charred carrots, and sesame seeds. Add kimchi or sambal oelek for extra heat if desired.