Using a wide vegetable peeler or mandolin, shave long, wide ribbons. Place them flat in a shallow dish or baking sheet and sprinkle lightly with flaky salt. Let sit 10-15 minutes. This draws out moisture and softens them, so they bend easily. Pat dry with a paper towel.
Cut haloumi into 1to1-½ inch cubes (about the width of the ribbons) and alternate with the threaded zucchini ribbons on the skewers. If using bamboo skewers, soak them for 15 minutes in water before using to prevent too much burning.
Aim for three ribbons and two pieces of haloumi on each. Pour olive oil into a bowl and, using a pastry brush, lightly brush both sides of the skewers. Sprinkle with pepper and salt.
Heat a grill pan or barbecue to medium-high. Grill skewers for 2–3 minutes per side until the haloumi is golden and has distinct char marks.
Transfer to a platter. Zest some lemon over the top, then slice lemon in half and squeeze the juice over as well. Scatter with parsley and serve warm.
