Pat the halloumi dry and slice into 0.5-inch planks.
In a bowl, whisk together olive oil, lemon juice, garlic, oregano, black pepper, red pepper flakes, and lemon zest.
Add the halloumi to the mixture and gently turn to coat. Marinate for 10 minutes while preheating a grill or grill pan to medium-high (about 425–450°F).
Clean and oil the grill grates. Use tongs and a folded paper towel lightly dipped in oil to wipe the grates.
Grill halloumi for 2 to 3 minutes per side until deep golden with grill marks and the edges are softly melted. Avoid overcooking.
Transfer to a platter, sprinkle with parsley, and serve immediately with lemon wedges.
Notes
Halloumi tastes best hot off the grill. Add to salads, grain bowls, or tuck into warm pita with tomatoes and cucumbers.