Place the nectarines in boiling water for 2 minutes, then rinse in cold water. Halve and stone the fruit, then quarter and peel. Possibly halve the quarters again. Prepare the fruits.
Finely chop the basil, mix with the oil and lemon zest and leave for 5 minutes. Then season the oil with salt, pepper and sugar.
Cut the burrata open and place in the middle of two plates. Spread the nectarine wedges around the burrata and drizzle everything with the basil oil.