Prepare the balsamic glaze (if making from scratch): Combine balsamic vinegar and honey in a small saucepan. Bring to a simmer over medium heat and reduce until the liquid coats the back of a spoon, about 5-7 minutes. Set aside to cool and thicken.

Preheat a grill or grill pan to medium-high heat. Lightly brush the cut sides of the nectarine halves with 1 tablespoon of olive oil and season lightly with salt and pepper.

Grill the nectarines cut-side down for 3-4 minutes until distinct grill marks appear and the fruit is slightly softened and caramelized. Remove from the grill and allow to cool slightly before slicing into wedges.

Assemble the salad base: In a large bowl, gently toss the arugula with a small drizzle of olive oil (about 1 teaspoon) and a light sprinkle of salt and pepper, if desired.

Arrange the dressed arugula on a serving platter. Artfully distribute the grilled nectarine wedges and torn pieces of burrata over the greens.

Drape the prosciutto slices artfully over the salad components. Drizzle the entire salad generously with the prepared balsamic glaze just before serving.

Serve immediately while the nectarines are still slightly warm for the best contrast in temperature and texture.