1In a small bowl, whisk together soy sauce, brown sugar, 1 tbsp sesame oil, minced garlic, ginger, and black pepper. Add sliced beef and onion, toss to coat evenly, and let sit for 10 minutes while you prepare everything else.
2In a small bowl, whisk rice vinegar with 1 tsp salt. Add julienned daikon and cucumber, toss gently, and set aside to quick-pickle.
3Heat a large skillet over medium-high heat. Working in two batches to avoid crowding, cook the beef mixture for 2–3 minutes per batch, stirring occasionally, until the edges are caramelized and the beef is cooked through. Transfer to a plate and tent loosely with foil to keep warm.
4Wipe the skillet clean, add a splash of water, and crack the 4 eggs into it. Cover and cook over medium heat until the whites are set but the yolks are still runny, about 3–4 minutes.
5Divide cooked rice among four bowls. Top each with a portion of bulgogi beef and onions. Add a runny egg to each bowl. Top with drained pickled vegetables, fresh scallions, cilantro leaves, and a pinch of sesame seeds. Serve right away.