For the rice pudding:

Split the vanilla pod in two, scrape off the seeds with the blade of a knife.
Rinse the rice in cold water. Place in a saucepan and cover with cold water. Bring to the boil and remove from the heat 2 to 3 minutes after the first bubbles appear. Rinse again and drain.
Bring the milk to the boil in a large saucepan. Reduce the heat, add the rice, the brown sugar, the vanilla seeds and the vanilla pod. Stirring continuously, dot with butter and continue to cook over a low heat for 30 to 40 minutes (depending on the rice used). The liquid should not be completely absorbed.

Wash the peaches, peel them, then halve and cut into cubes.
Melt the butter in a frying pan, add the peach cubes, sprinkle with sugar and cook at a moderate heat until caramelised.
Crumble the biscuits.

Serve the rice with the sautéed peaches, sprinkle with the crumbled Gavottes and enjoy!