In a bowl, whisk together soy sauce, brown sugar, sesame oil, garlic, ginger, rice vinegar, and gochujang. Add the chicken thighs and marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
Heat vegetable oil in a large skillet over medium-high heat. Remove chicken from marinade and cook for about 6-8 minutes per side, or until cooked through and caramelized. Remove from heat and let rest for a few minutes before slicing.
While the chicken is resting, warm the tortillas in a dry skillet or microwave until pliable.
Slice the chicken into strips and assemble the tacos by placing a few strips of chicken on each tortilla. Top with shredded cabbage, diced cucumber, green onions, and cilantro.
Serve with lime wedges on the side for squeezing over the tacos.