Heat vinegar in saucepan over medium until it begins to simmer. Reduce heat to medium-low, stirring occasionally. Gently simmer until liquid is reduced to ¼ cup and has a syrupy consistency, about 20 minutes. Be sure to turn on your fan or open your windows while this reduces, and take care not to inhale the fumes!
Meanwhile, heat large cast iron or heavy-bottomed pan over medium-high heat. Spread walnuts evenly in pan and toast about 5 minutes, stirring once or twice.
Prepare your salad ingredients and add everything but peaches and vinegar to a large salad bowl. Toss gently to combine. Serve salad and top with peach slices and a drizzle of the balsamic reduction.
Notes
If you want leftovers, store salad separately from peaches and reduction. When ready to serve, cut a fresh peach and drizzle with balsamic.