Slice the peaches in half by cutting around the pit and twisting gently, like you would an avocado. Remove the pit with the help of a spoon and brush the cut sides with olive oil.
Lightly brush a grill pan (or outdoor grill) with olive oil and set it over medium-high heat. Allow it to get hot before adding the peaches — this helps achieve those lovely, defined grill marks.
Place the peach halves cut-side down on the hot grill pan. Let them cook undisturbed for about 5 minutes, or until you see deep grill marks and the peaches start to soften slightly. You’ll know they’re ready when the surface caramelizes and lifts easily from the grill.
Flip the peaches carefully and grill for 1 more minute on the skin side. They should be tender but still hold their shape — avoid overcooking, as they’ll become mushy.
Remove the peaches from the grill and transfer them to a plate. Let them cool completely to avoid wilting the greens later. Once cooled, slice each half in half again to create four wedges per peach.
In a small mixing bowl, combine the balsamic vinegar, chili flakes, lime juice, and salt. While whisking steadily, slowly drizzle in the olive oil to emulsify the dressing. Set aside at room temperature until ready to use. (Tip: If making ahead and refrigerating, bring it out 20 minutes before serving to let the oil return to liquid form.)
In a large serving bowl, lay down a bed of fresh baby arugula. Gently tuck in the grilled peach wedges, followed by the fresh blueberries and crumbled feta. Sprinkle with the pecans and basil leaves. Drizzle with the balsamic vinaigrette just before serving, and give everything a gentle toss or leave it composed for a stunning presentation.