Toast the pecans: Place the pecans in a dry skillet over medium heat and cook for 3 to 5 minutes, stirring often, until fragrant. Set aside to cool.
Make the dressing: Whisk together the olive oil, balsamic vinegar, honey, Dijon mustard, salt, and black pepper in a small bowl.
Assemble the salad: Add the arugula, peach wedges, red onion, and basil to a large bowl.
Toss gently: Pour over half of the dressing and toss carefully until the leaves are lightly coated.
Finish and serve: Add the feta and toasted pecans, drizzle with more dressing if needed, and serve immediately.