Whisk together balsamic vinegar, honey, Dijon mustard, minced garlic, salt, and pepper in a bowl. Gradually drizzle in olive oil while whisking to emulsify the vinaigrette. Reserve half as a marinade for chicken.

Combine chicken thighs with the reserved vinaigrette in a large bowl. Cover and marinate in the refrigerator for at least 30 minutes, or up to 2 hours.

Preheat the grill to medium-high heat. Grill the chicken for 6-8 minutes on each side, brushing with barbecue sauce during the last few minutes until fully cooked.

While grilling chicken, cut peaches in half and remove pits. Brush the cut sides with olive oil and grill cut-side down for 3-5 minutes until marked and tender.

Preheat the oven to 425°F. Cube the croissants and toss with olive oil, salt, and pepper. Bake for 5-8 minutes until golden and crispy.

Cook prosciutto in a pan over medium heat until crispy, about 3-4 minutes, then drain on paper towels.

In a large serving bowl, toss arugula with reserved balsamic vinaigrette. Arrange chicken, grilled peaches, burrata, prosciutto, and croissant croutons on top. Garnish with fresh basil and serve with extra barbecue sauce.