Preheat the grill to medium-high heat, approximately 400 degrees Fahrenheit.

In a blender or small food processor, combine the basil leaves, 1/4 cup extra-virgin olive oil, white balsamic vinegar, honey, Dijon mustard, salt, and pepper; blend until the vinaigrette is emulsified and smooth.

Lightly brush the cut surfaces of the peach halves with 1 tablespoon of olive oil to prevent sticking.

Place the peaches cut-side down onto the hot grill grates and cook undisturbed for 3 to 5 minutes until caramelized grill marks appear and the fruit softens slightly.

Remove the peaches from the grill and slice each half into three wedges.

Distribute the baby arugula across a large platter or four individual plates.

Layer the grilled peach wedges, crumbled goat cheese, toasted pecans, and red onion slices over the greens.

Drizzle the basil vinaigrette evenly over the salad components and serve immediately.