If using wooden skewers, soak them in water for at least 30 minutes.
Cut the halloumi and vegetables into evenly sized pieces.
In a large bowl, combine the olive oil, lemon juice, garlic, oregano, salt, and black pepper.
Add the halloumi and vegetables, then gently toss until everything is evenly coated.
Thread the halloumi and vegetables onto the skewers, alternating the ingredients.
Preheat an outdoor grill or grill pan over medium-high heat.
Grill the skewers for 8-10 minutes, turning every 2-3 minutes until the halloumi is golden and the vegetables are lightly charred and tender.
Garnish with fresh parsley, serve with lemon wedges, and enjoy immediately.