Preheat oven to 350 degrees. On a large baking sheet, create a ring by laying out the crescent roll dough with the largest ends to the inside of the ring. You will have a small circle in the middle and the sides of each crescent dough piece will overlap a little.
Slice the brie into pieces and lay along the inside of the ring. Top with peach slices and basil leaves. Fold narrow end of the crescent dough towards the center covering the peaches.
Bake in preheated oven for 12-15 minutes or until lightly browned. Remove from oven.