Brush the cut side of the peaches with olive oil and use the remaining on the slices of bread.
Place the peaches cut side down on the grill using indirect heat. Add the bread butter side down as well over indirect heat. Cook the peaches for 3 minutes or until they have softened and the bread is toasted.
Seasoning the peaches
Once the peaches are cool enough to handle slice each half into eighths.
In a mixing bowl combine the peach slices, salt, red pepper flakes, mint, almond slices, and ½ tablespoon of honey. Toss to combine.
Assembly
Slice the burrata and place a small slice on the toast followed by the peaches. Drizzle with the remaining honey and the balsamic vinegar.