Preheat the grill to medium-high heat.
Brush the cut sides of the peach halves with a little olive oil.
Place the peaches cut-side down on the grill and cook 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 arugula, crumbled feta, and toasted walnuts.
In a small bowl, whisk together the olive oil, balsamic vinegar, honey, salt, and pepper to create the dressing.
Slice the grilled peaches and add them to the salad mixture.
Drizzle the dressing over the salad and toss gently to combine.
Serve immediately, garnished with additional feta or walnuts if desired.