Preheat a grill pan or outdoor grill over medium heat.
Brush peach halves lightly with olive oil and place cut-side down on the grill until charred and softened, about 3-4 minutes.
Remove peaches and slice into wedges.
Toast baguette slices on the grill until crisp and golden.
Spread or place a generous portion of burrata on each slice of toasted bread.
Top with grilled peach slices, drizzle with honey, and scatter fresh basil leaves.
Finish with a pinch of salt and black pepper before serving.