Preheat your grill to medium-high heat, and brush the grates lightly with oil to prevent sticking.
Halve the peaches and remove the pits, then brush the cut sides generously with olive oil, ensuring they are evenly coated.
Place the peaches cut side down on the hot grill, listening for that satisfying sizzle; cook for about 3-4 minutes until grill marks appear and the skins blister and char slightly.
Flip the peaches carefully and cook for another 3-4 minutes, until they soften slightly and develop deep golden-brown grill lines.
Remove the peaches from the grill and let them rest for a couple of minutes; this helps them soften further and makes slicing easier.
Slice the grilled peaches into wedges or thick slices, revealing their tender, caramelized interiors with smoky edges.
Arrange the arugula on a serving platter, then top with the warm grilled peach slices and sprinkle with crumbled feta cheese.
Garnish the salad with fresh mint or basil leaves for a burst of herbal brightness.
Drizzle the balsamic glaze over the top, adding a sweet-tangy finish that complements the smoky peaches.
Finish with a sprinkle of salt and freshly cracked pepper to taste, then serve immediately and enjoy the vibrant flavors and textures.
