Wash and dry 4 cups baby arugula thoroughly using a salad spinner, then pat with paper towels to remove any remaining moisture.
Toast 1/3 cup pecans or walnuts in a dry skillet over medium heat for 3-4 minutes until fragrant, stirring frequently. Let cool completely, then roughly chop.
Prepare the dressing by whisking together 3 tablespoons olive oil, 2 tablespoons balsamic vinegar, 1 tablespoon honey, salt, and pepper in a small bowl. Alternatively, shake in a jar with a tight lid until well combined.
Slice 3 ripe peaches into wedges, removing the pit. Thinly slice 1/4 red onion and tear 1/4 cup fresh basil leaves.
Assemble the salad by placing arugula in a large bowl. Top with peach wedges, 1 cup mozzarella pearls, red onion slices, toasted nuts, and basil.
Drizzle with dressing just before serving and toss gently to combine. Season with additional salt and pepper if needed.