Preheat your grill or grill pan to medium-high heat. Brush the peach halves with olive oil and place them cut-side down on the grill. Cook for 2-3 minutes until you see grill marks and the peaches begin to soften. Flip and grill for another 1-2 minutes. Remove from the grill and let them cool slightly.

In a small saucepan, combine the balsamic vinegar and honey. Simmer over low heat for 5-7 minutes, stirring occasionally, until the mixture thickens into a syrupy glaze. Remove from heat and let it cool.

Arrange the grilled peach halves on a serving platter. Tear the burrata cheese into chunks and place it around the peaches. Drizzle the balsamic glaze over the top, and scatter fresh basil leaves on the salad. Season with salt and freshly ground black pepper to taste. If desired, sprinkle with toasted pine nuts or almonds for added crunch.