In a medium bowl, whisk together the gochujang, tamari, honey, sesame oil, minced garlic, and grated ginger to create the marinade.
Cut the pork shoulder into 1-inch cubes and toss them in the marinade until thoroughly coated; let sit for 15 minutes.
Preheat a grill or grill pan over medium-high heat and lightly grease with a touch of oil if necessary.
Thread the marinated pork cubes, zucchini rounds, and red bell pepper pieces onto skewers, alternating for even cooking.
Grill the skewers for 10 to 12 minutes, turning every few minutes, until the pork is cooked through and the glaze is bubbly and dark.
Remove from the heat and sprinkle with toasted sesame seeds and fresh green onions before serving warm.