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.

In a large bowl, toss the arugula with a drizzle of olive oil, salt, and pepper. Arrange the arugula on a serving platter or individual plates. Place the grilled peach halves on top of the arugula.

Tear the burrata cheese into chunks and scatter it over the peaches and arugula. Drizzle the balsamic glaze over the salad, then sprinkle with fresh basil and toasted pine nuts or almonds.