Heat your grill to medium-high heat (around 400°F if you're using a grill thermometer). Pat the peach halves dry with paper towels—this helps them get that gorgeous golden crust instead of steaming. Brush them lightly with a tiny bit of olive oil on the cut side. You want them prepped and ready to go because they grill fast.
Place peaches cut-side down on the grill grates and grill for 3-4 minutes without moving them. You're looking for those beautiful char marks to appear. If you try to flip them too early, they'll stick like crazy and fall apart, so patience here is everything.
Flip the peaches carefully using tongs and grill the other side for another 2-3 minutes until they're heated through and tender. The peaches should feel soft when you gently press them, but not mushy. Remove them to a cutting board and let them cool for just a minute—they'll be hot.
Slice the grilled peaches into bite-sized pieces while they're still warm. I usually cut each half into 4-5 wedges. Don't worry if some pieces break a little—that's totally normal and honestly adds to the rustic charm of this elegant summer salad.
Whisk together the olive oil, honey, lemon juice, salt, and black pepper in a small bowl. Taste it as you go because you might want more lemon or salt depending on your preference. This simple dressing is the MVP of this grilled peach arugula salad recipe.
Place the fresh arugula in a large serving bowl or on individual plates. Add the grilled chicken strips if you're using them for extra protein. Drizzle about half the dressing over the greens and toss gently to coat.
Top with warm grilled peach slices, crumbled feta, and toasted nuts. Drizzle the remaining dressing over everything right before serving. Serve immediately while the peaches are still warm—that contrast between warm fruit and cool greens is what makes this dish shine.