In a glass jar or liquid measuring cup, combine olive oil, vinegar, hot honey, garlic, and ½ tsp. salt; mix well to combine. Set aside.
Grill peach segments in a well-oiled grill pan, outdoor grill, or skillet over medium heat until nicely caramelized with grill marks, about 2 to 3 minutes per side.
Slice corn from the cobs and add to a large mixing bowl (the corn stays raw). Add shallots, basil, mint, and half of the hot honey dressing; toss to combine.Transfer corn mixture to a serving platter and top with grilled peach segments and dollops of burrata cheese. Sprinkle salad with a pinch more salt (especially the dollops of burrata). Drizzle remaining dressing overtop, and garnish with chopped pistachios and additional fresh basil.
