In a mixing bowl, whisk together the olive oil, white balsamic vinegar, honey, minced garlic, basil, and mint until well combined. Season with salt and pepper to taste.

Preheat the grill to medium-high heat. Brush the peach halves with a little olive oil and place them cut-side down on the grill. Grill for about 4-5 minutes until grill marks appear and the peaches are slightly softened.

On a serving platter, arrange the mixed greens. Top with grilled peach halves, slices of burrata, and sprinkle with toasted walnuts. Drizzle with the basil mint vinaigrette.