Preheat your oven to 400°F (200°C). Arrange the baguette slices on a baking sheet and brush both sides lightly with olive oil.
Bake the baguette slices in the preheated oven for about 5-7 minutes, or until they are golden and crispy. Remove from the oven and let cool slightly.
While the bread is baking, prepare the burrata. Gently tear the burrata cheese into smaller pieces and place it in a bowl. Season with a pinch of salt and pepper.
Once the crostini have cooled, spread a generous amount of burrata on each slice.
Top the burrata with slices of prosciutto and peach. Drizzle with balsamic glaze and a little extra olive oil if desired.
Garnish with fresh basil leaves before serving. Enjoy immediately while the crostini are still warm.