Combine gochujang, white sugar, 1 tablespoon sesame seeds, and 2 teaspoons sesame oil in a small bowl to make a seasoned gochujang paste.
Whisk vinegar, soy sauce, 1 teaspoon toasted sesame oil, and instant beef stock together in a large bowl. Stir in seasoned gochujang paste. Add cucumbers; stir until coated. Sprinkle with 1 tablespoon toasted sesame seeds.
Let cucumbers marinate in the refrigerator before serving, at least 1 hour.