Preheat grill pan or outdoor grill to medium-high heat. Brush peach slices lightly with 1 tablespoon olive oil and season with a pinch of salt.
Grill peach slices for 2-3 minutes per side until caramelized and tender with nice grill marks. Remove and set aside.
Toast bread slices until golden brown and crispy on both sides.
Tear burrata into generous pieces and distribute evenly over the warm toast slices.
Top each toast with grilled peach slices, arranging them attractively over the cheese.
Drizzle with remaining olive oil and honey if using. Season with salt and pepper to taste.
Garnish with torn fresh basil leaves and serve immediately while toast is still warm.
Notes
Storage tip: Grilled peaches can be made up to 2 days ahead and stored in the refrigerator. Bring to room temperature before serving. For best results, use peaches that are ripe but still firm. The burrata should be at room temperature for optimal creaminess.