Preheat the grill to medium heat. Brush the cut sides of the peach halves with olive oil and sprinkle with 1/2 teaspoon of salt.
Place the peaches cut-side down on the grill. Grill for about 4-5 minutes until grill marks appear and the peaches are slightly softened. Remove from the grill and let cool slightly.
In a large bowl, combine the mixed salad greens, blueberries, crumbled feta cheese, and chopped walnuts or pecans.
Slice the grilled peaches into wedges and add them to the salad mixture.
Drizzle the balsamic vinaigrette over the salad and toss gently to combine. Season with the remaining 1/2 teaspoon of salt, if desired.
Serve immediately, or chill in the refrigerator for up to 30 minutes before serving for a refreshing touch.