Slice the peaches in half and remove the pit. Cut each peach into 8 thick wedges.
Brush the peaches with olive oil and season with salt and pepper.
Make sure your grill grates are well cleaned and lightly oil with vegetable oil. Preheat to medium high.
Place the peaches on the grill. Cook for 2 minutes per side without moving. When done, remove them from the grill and let cool. If you don’t have a grill, cook the peaches on a grill pan on the stovetop.
In a sealable jar, combine the olive oil, vinegar, honey, lemon juice and zest, garlic, and half of the fresh herbs. Shake until well combined.
Arrange the mixed greens on a serving platter. Layer on the grilled peaches and tomatoes.
Cut the burrata into 6 pieces. If it’s especially runny, you can blot it with a paper towel before placing it on the salad. Arrange the pieces around the salad.
Sprinkle on the pistachios.
Drizzle the prepared vinaigrette over the salad.
Garnish with the remaining fresh herbs.