Heat a skillet to medium-high heat. Brush the ciabatta liberally with olive oil.
Place each slice of bread face-down on the skillet and toast until they are golden brown, about 1-2 minutes max.
Dice up the peach, chiffonade the basil, chop the pistachios finely and add all the ingredients to a bowl. Squeeze in the lemon juice and toss to coat.
When the bread has toasted, spread the burrata on top.
Top the toast with the peaches mixture, plus more basil for garnish. Eat immediately!