Preheat your grill or grill pan to medium-high heat (about 400°F). If using a grill pan, place it over medium-high heat for 3-4 minutes until very hot.

Pat the halloumi slices completely dry with paper towels. Brush both the cut sides of the peaches and both sides of the halloumi with 1 tablespoon of olive oil.

Place the halloumi slices on the hot grill. Cook undisturbed for 2-3 minutes until golden grill marks form and the cheese releases easily. Flip and cook another 2 minutes. Transfer to a plate.

Place the peach halves cut-side down on the grill. Cook for 3-4 minutes until caramelized and grill marks appear. Flip and cook 1-2 minutes more until slightly softened but still holding their shape.

Arrange the baby arugula on a large serving platter or divide among 4 plates. Drizzle with the remaining 1 tablespoon of olive oil. Slice the grilled halloumi into strips or leave as slabs.

Arrange the grilled peach halves and halloumi over the arugula. Scatter the torn basil and toasted pine nuts over the top.

Drizzle generously with balsamic glaze. Sprinkle with flaky sea salt and freshly cracked black pepper. Serve immediately while the peaches and halloumi are still warm.