Step 1: Prepare the Pistachio Pesto

1. In a food processor, combine fresh basil leaves, shelled pistachios, grated Parmesan cheese, and garlic.
2. Pulse the ingredients a few times until roughly chopped.
3. Gradually add the olive oil while blending until the mixture becomes smooth. You may need to scrape down the sides of the processor a few times.
4. Add lemon juice, and season with salt and pepper to taste. Blend again until everything is well combined.
5. Transfer the pesto to a small bowl and set it aside.

Step 2: Grill the Peaches

1. Preheat your grill or a grill pan over medium-high heat. Lightly brush the peach halves with olive oil to prevent sticking.
2. Place the peaches cut-side down on the grill and cook for about 3-4 minutes, or until grill marks appear and the peaches have softened slightly.
3. Remove the peaches from the grill and set them aside to cool slightly.

Step 3: Assemble the Salad Base

1. Arrange the mixed greens evenly on a large serving platter.
2. Tear the burrata cheese into pieces and place them strategically over the greens.
3. Arrange the grilled peach halves on top of the greens and cheese.

Step 4: Add Fresh Herbs and Garnishes

1. Sprinkle the fresh basil leaves and chopped toasted pistachios over the salad for added freshness and crunch.

Step 5: Drizzle with Pistachio Pesto and Balsamic Glaze

1. Generously spoon the pistachio pesto over the salad, making sure to cover the peaches and burrata.
2. Lightly drizzle with balsamic glaze for a hint of tangy sweetness.
3. Finish with a pinch of sea salt and a few cracks of black pepper to taste.