In a bowl, whisk together soy sauce, olive oil, honey, apple cider vinegar, garlic, paprika, and black pepper. Add the pork cubes, toss to coat, cover, and refrigerate for at least 30 minutes (or up to 4 hours for deeper flavor).
Prepare the Skewers
If using wooden skewers, soak them in water for at least 30 minutes to prevent burning. Thread marinated pork, bell peppers, onions, and zucchini, onto the skewers, alternating ingredients for even cooking.
Preheat the Grill
Heat the grill to medium-high (around 400°F). Lightly oil the grates to prevent sticking.
Grill the Kabobs
Place skewers on the grill and cook for about 10-12 minutes, turning occasionally, until the pork is cooked through (internal temperature of 145°F).
Glaze with BBQ Sauce
During the last 2-3 minutes of grilling, brush the kabobs generously with BBQ sauce, turning to coat evenly. Let the sauce caramelize slightly for a rich, smoky flavor.
Rest and Serve
Remove the skewers from the grill and let them rest for 5 minutes. Serve hot with extra BBQ sauce on the side.