Cut a little off the upper and lower part of the potatoes, scoop out the insides using a melon baller, leaving a border of approx. 3 mm. Cook the potatoes (uncovered) in boiling salted water for approx. 15 mins. until soft. Drain the potatoes, allow to cool slightly, transfer to a plate.
Mix the burrata, oil, crème fraîche and salt, stuff the potatoes with the mixture. Top with the caviar and basil leaves.