Brush flatbread with olive oil and sprinkle with shredded mozzarella (or preferred Italian cheese blend). Toast lightly in a toaster oven to melt the cheese.
Tear prosciutto and burrata into smaller pieces. Place peach slices, prosciutto, and burrata across flatbread, as evenly spaced out as possible.
Toast again for 3-5 minutes, just enough to warm peaches and burrata.
Remove from toaster oven, top with arugula, and drizzle with balsamic vinegar if desired.
Slice and serve.