Preheat oven to 300 degrees F. On a lightly floured surface, roll all 4 puff pastry sheets to fit a 9 x 11 baking dish; set aside. Grease pan with room temperature butter. Place 1 rolled sheet of puff pastry into pan then grease pastry sheet with butter. Place another layer of puff pastry on top, then grease with butter.
In medium bowl, combine coarsely chopped pistachios, honey, sugar and water and mix. Pour mixture over puff pastry sheets in dish. Place another puff pastry sheet over the top of the mixture, then grease it with butter. Place the last puff pastry on top and pour remaining butter on top. Use a sharp knife to cut baklava in the shape of a diamond or square.
Place baklava in oven and bake for 90 minutes. The top of the puff pastry should be light golden color and the papers should appear crispy. Meanwhile, grind or chop the remaining pistachios into an almost fine dust or finely chopped. Allow baklava to cool then garnish with pistachios.