Preheat your grill or grill pan to medium-high heat until hot, with a slight sizzle when peaches are placed on it.
Brush the cut sides of the peaches lightly with olive oil to prevent sticking and promote caramelization.
Place the peaches cut-side down on the grill, pressing gently to ensure contact, and cook for about 4–5 minutes until grill marks appear and the fruit softens slightly.
Flip the peaches carefully and cook for another 3–4 minutes, watching for deep char lines and a soft, yielding texture. Remove from grill and let cool slightly.
While the peaches cool, whisk together lemon juice, honey, and balsamic vinegar in a small bowl to make the vinaigrette.
In a large mixing bowl, toss the greens with the vinaigrette until evenly coated, then transfer to serving plates.
Slice the grilled peaches into wedges and arrange them on top of the dressed greens, distributing evenly for a colorful presentation.
Sprinkle the crumbled feta and toasted nuts over the top, adding a salty crunch to each bite.
Garnish the salad with chopped fresh basil or mint for a burst of herbal brightness.
Serve immediately to enjoy the warm, smoky peaches against the crisp greens, or refrigerate briefly if needed, then toss gently before serving.