Cut the halloumi into approximately 1-inch cubes, large enough to slide onto skewers without falling apart (see notes for more tips). Keep the tomatoes intact, cut the red onion and pepper into squares, and slice the zucchini into ½-inch thick circles. Try to make the veggies a similar size and thickness for even cooking.
In a large bowl, whisk together the extra virgin olive oil, lemon juice, garlic, oregano, parsley, black pepper, and salt.
Place the veggies in the bowl with the marinade and toss until coated. Cover with plastic wrap or a reusable bowl wrap. Refrigerate for at least 30 minutes and up to 12 hours in advance.
Thread 12 flat metal skewers with the marinated veggies and halloumi.
Preheat the grill to medium for 10 minutes. Scrape it clean of debris if needed, then grease it generously. Saturate a folded paper towel with avocado oil. Hold it with grill tongs and spread it across the grates until they are evenly coated.
Cook under the grill for 8 to 15 minutes, rotating every 2 to 3 minutes (using grill tongs to avoid burning yourself), until the veggies are tender and lightly browned and the cheese is golden brown with slightly blistered char marks. Keep a close eye to avoid burning. If the veggies are charring too quickly, reduce the heat to medium-low.
Carefully remove the skewers from the grill using tongs, oven mitts, or grill gloves.
Serve with pesto, chimichurri, yogurt sauce, balsamic glaze, or other dipping sauces. These pair well with rice and warm pita or on the side of grilled chicken.
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