In a small bowl, whisk together the gochujang, tamari, sesame oil, honey, minced garlic, and grated ginger to create the marinade.
Cut the pork shoulder into 1-inch cubes and toss them in half of the marinade, allowing them to sit for at least 15 minutes.
Chop the red bell pepper and zucchini into bite-sized chunks similar in size to the pork pieces.
Thread the marinated pork, bell peppers, and zucchini onto skewers, alternating between the meat and vegetables.
Preheat a grill or grill pan over medium-high heat and lightly grease to prevent sticking.
Grill the skewers for 8 to 10 minutes, turning occasionally to ensure even cooking and a nice char on all sides.
Brush the remaining marinade onto the skewers during the final 2 minutes of grilling.
Remove from the heat and garnish with sesame seeds before serving hot.