01 - Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Drain, rinse under cool water, and set aside.
02 - Preheat a grill or grill pan over medium-high heat. Lightly brush peach halves with olive oil. Grill for 2 to 3 minutes per side until marked and caramelized. Allow to cool slightly, then cut into wedges.
03 - In a small bowl, whisk together olive oil, white balsamic vinegar, honey, Dijon mustard, salt, and pepper until emulsified.
04 - Combine cooked pasta, grilled peach wedges, arugula or baby spinach, sliced shallot, and most of the torn basil in a large salad bowl. Drizzle with vinaigrette and toss gently to coat.
05 - Tear burrata into large pieces and arrange on top of the salad. Sprinkle with toasted pine nuts or walnuts and the remaining basil leaves.
06 - Serve immediately or refrigerate for up to 1 hour before serving for a chilled dish.