Preheat the grill or grill pan over medium heat.
Slice the peaches in half and remove the pits. Brush the cut sides lightly with olive oil.
Grill the peach halves, cut side down, for about 4 minutes until you have nice grill marks and the peaches soften slightly. Remove from the grill and let cool.
While the peaches are cooling, brush the baguette slices with olive oil on one side and place them on the grill. Toast for about 2-3 minutes on each side or until golden brown and crisp.
Cut the grilled peaches into slices.
On the toasted side of each crostini, place a piece of burrata cheese and top it with a few slices of grilled peaches.
Drizzle with balsamic glaze, season with fresh thyme, salt, and pepper.
Arrange the crostini on a serving platter and serve immediately.