For the phyllo layers: Heat the oven to 375 degrees F. Lay a sheet of phyllo pastry on a work surface. Brush with melted butter. Sprinkle over about a teaspoon of sugar and some hazelnuts. Make 3 more layers the same way. Using a large knife or pizza cutter, slice the sheet into 8 rectangles. Arrange on a baking sheet and bake until golden and crisp, about 7 minutes.
For the blackberry filling: Whip the cream with enough syrup to sweeten, and the vanilla extract. Assemble the dessert just before serving: Lay a phyllo layer on each of 4 plates. Top each with 1/4 of the cream mixture. Arrange berries standing upright on top. Top each dessert with another round of phyllo. Serve.