Preheat the grill to its highest setting. Heat a griddle pan until smoking.
Drizzle the peaches with the olive oil and place cut-side down into a hot griddle pan and chargrill for 2-3 minutes, or until golden-brown. Transfer to serving plates and set aside in a warm place.
For the sabayon, place the egg yolks, sugar and wine into a bowl placed over a saucepan of simmering water. Whisk vigorously and constantly until the mixture becomes thick and foaming.
Add the fresh basil and fold through the mixture.
Place the peaches onto a baking sheet. Spoon the sabayon over the peaches and place under the grill to cook for three minutes, or until golden brown.
Place the peaches onto a plate and serve.