Preheat your grill or grill pan to medium-high heat. Brush the peach halves lightly with olive oil. Place them cut-side down on the grill and cook for 2-3 minutes until they develop grill marks and soften slightly. 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 slightly and becomes syrupy. 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 peaches and burrata. Scatter fresh basil leaves on top and season with salt and freshly ground black pepper. Garnish with toasted pine nuts or almonds if desired.