Preheat the oven to 400 degrees . Lay the pastry on a floured work surface and cut into 3 strips. Cut each strip crosswise into 3 squares. Arrange the 9 squares on a baking sheet, brush with the butter and sprinkle 1 tablespoon sugar on top. Bake until golden, 15 minutes. Let cool.
In a bowl, sprinkle the nectarine slices with 1 tablespoon sugar; toss.
In another bowl, whip the cream, remaining 1 tablespoon sugar and vanilla until stiff.
Split each puff pastry square into 2 layers. Top each with whipped cream and nectarines.