Preheat your grill to medium-high heat, ensuring the grates are clean and lightly oiled to prevent sticking.
Slice the peaches in half, remove the pits, and lightly brush the cut sides with a little olive oil to help prevent sticking and promote caramelization.
Place the peaches cut-side down on the hot grill. Let them cook for about 3-4 minutes until you see deep grill marks and the edges start to turn a golden amber color.
Flip the peaches carefully with tongs and cook for another 2-3 minutes until the other side has similar grill marks and the flesh begins to soften.
Remove the peaches from the grill and let them rest for a couple of minutes to cool slightly, making them easier to handle.
While the peaches rest, place the greens in a large bowl, drizzle with the remaining olive oil, and toss gently to coat evenly.
Slice the grilled peaches into thick wedges, revealing the caramelized, smoky flesh inside.
Add the sliced peaches to the greens, then sprinkle crumbled feta cheese and chopped mint over the top.
Drizzle the balsamic glaze over the salad just before serving for a tangy and sweet finish.
Gently toss the salad to combine everything, then serve immediately to enjoy the smoky, juicy peaches with the fresh greens and salty feta.