In a large skillet over medium-high heat, add the ground beef. Cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain excess fat if necessary.
Stir in the soy sauce, sesame oil, gochujang, brown sugar, minced garlic, and minced ginger. Cook for an additional 3-4 minutes until the beef is well coated and heated through. Season with salt and pepper to taste.
In a separate bowl, combine the sliced cucumber, julienned carrot, rice vinegar, and half of the chopped green onions. Toss to combine and let sit for about 5 minutes to allow the flavors to meld.
Serve the spicy ground beef over a bed of the cucumber salad. Garnish with the remaining green onions and sprinkle with sesame seeds.