Grill, uncovered, until well charred (about 4 minutes) turning to repeat on all sides. In a bowl combine lemon juice, vinegar, honey, coarse salt, and ground pepper. Whisk, until salt and honey have dissolved. Add oil and whisk until thoroughly combined.
Arrange arugula on plates or platter, drizzle with vinaigrette, top with toasted pine nuts, burrata, and warm grilled peaches.