Preheat your grill to medium-high heat (around 400°F) and let the grates get properly hot before you place anything on them. I used to skip this step and ended up with peaches that stuck instead of releasing—patience here means the difference between a dish that screams summer and one that falls apart.
Pat your peach quarters completely dry with paper towels, then brush them lightly with 1/2 tbsp of olive oil on both sides. Wet fruit steams instead of chars, so this single step transforms the final result because the oil creates the surface contact needed for caramelization.
Grill the peaches cut-side down for 3-4 minutes until you see dark char marks forming—they should release easily when ready to flip. I wait for that moment when they're no longer sticking because that's your signal the sugars have begun to concentrate; flip and grill the skin side for 2 minutes.
Remove the peaches and let them cool on a plate for 5 minutes—they'll continue to cook slightly from residual heat. This brief rest means the fruit stays firm enough to slice instead of falling into a puree when you cut it.
While peaches cool, combine honey, lemon juice, Dijon mustard, remaining 1.5 tbsp olive oil, sea salt, and black pepper in a small bowl. Whisk until the mustard fully dissolves and the dressing emulsifies because the acid and oil need to bond for proper coating.
Toss the arugula and spinach with most of the dressing in a large bowl—I keep some dressing back because hot peaches will release juice and thin it out. This move prevents the greens from sitting in puddle-thick dressing that makes them wilt beyond recovery.
Arrange dressed greens on a serving platter, then add the grilled peach slices, red onion, toasted walnuts, feta, and fresh mint. The warm peaches will gently soften the greens' edges without turning them to mush when you plate this way.
Drizzle with reserved dressing and top with sliced grilled chicken strips if serving as a main course for this crowd grilled fruit salad that everyone raves about at the cookout.