In a Pyrex or microwave-safe measuring cup, combine gochujang paste, apple cider vinegar, soy sauce, fish sauce, garlic, ginger, sesame oil, and sugar and microwave in 1-minute increments, stirring each time until well combined.
Cut the bottom off the romaine heart, separate and stack the leaves and set aside.
In a large skillet, brown ground beef until cooked through over high heat.
Add sauce to ground beef and turn the temperature down to low, mixing constantly.
Add broccoli slaw and carrots to the skillet and mix for 2 to 3 additional minutes.
Sprinkle the wraps with some toasted sesame seeds on top, and serve immediately with the stack of romaine leaves.