Cut peaches in half and remove pits. Brush each half with 1 teaspoon olive oil on both sides, then season lightly with salt and black pepper.
4 count ripe peaches, 3 tbsp olive oil, salt and black pepper
Preheat grill to medium-high heat. Place peach halves cut-side down on grill. Grill for 3-4 minutes without moving until char marks appear. Flip and grill another 3-4 minutes until softened but holding shape. Remove and let rest 2 minutes.
4 count ripe peaches
While peaches grill, toast pine nuts or walnuts in a dry skillet over medium heat for 3-4 minutes, stirring frequently, until fragrant and golden. Transfer to a plate to cool.
0.25 cup pine nuts or walnuts
Spread arugula or mixed greens on a platter or serving bowl. Slice grilled peaches into wedges and arrange over greens while warm.
4 cups arugula or mixed greens, 4 count ripe peaches
Tear burrata into large chunks and scatter over salad. Drizzle balsamic glaze in thin ribbons over everything. Top with toasted nuts, torn basil leaves, and a final sprinkle of salt and pepper. Serve immediately.
8 oz burrata cheese, 2 tbsp balsamic glaze, 0.25 cup pine nuts or walnuts, 0.25 cup fresh basil leaves, salt and black pepper