Preheat your grill or grill pan to medium heat.
Slice peaches in half (for outdoor grill) or quarters (for grill pan).
Brush the cut sides of peaches with butter or ghee and sprinkle with coconut sugar.
Grill peaches for 2-3 minutes per side until caramelized and grill marks appear.
In a small pot, simmer balsamic vinegar over medium heat for about 5 minutes until slightly thickened. Let cool.
On each plate, arrange a handful of arugula, add grilled peach slices, and tear burrata into chunks over the top.
Sprinkle with pine nuts, drizzle with olive oil and balsamic reduction, and finish with freshly cracked black pepper.