Prepare cucumber daikon slaw. Combine sliced cucumber, julienned daikon, and chopped scallions in a large bowl. Whisk together apple cider vinegar, water, sugar, and fish sauce in a medium bowl until sugar dissolves. Pour dressing over cucumber mixture, tossing to coat. Let sit for at least 10 minutes, tossing after 5 minutes.
Heat oil in a large saute pan over medium high heat. Add ground beef and spread in a single layer. Let cook undisturbed for 3 minutes or until the bottom of the beef starts to brown. Break up the meat with a wooden spoon into small chunks.
Add chopped onion and garlic, stirring to combine. Continue to saute until vegetables soften, about 4-5 minutes.
Add water, ketchup, gochujang, soy sauce, brown sugar, rice vinegar, Chinese mustard, and sesame oil, stirring until well combined. Reduce heat to low and simmer until the water evaporates, about 5-6 minutes. Adjust seasoning with salt and pepper.
Assemble sandwiches. Pile ground beef on the bottom of the buns. Toss the cucumber slaw once more and top beef with slaw. Finish with remaining buns and serve immediately.
Notes
You can make the cucumber daikon slaw up to 24 hours in advance. The longer it sits, the more pickled it will taste.